en>Headbomb: Various citation cleanup + AWB fixes, typo(s) fixed: , → , using AWB

2014-08-20T16:35:43Z

Various citation cleanup + AWB fixes, typo(s) fixed: , → , using AWB

← Older revision		Revision as of 18:35, 20 August 2014
Line 1:		Line 1:
	~~In mathematics~~, a '''nuclear C-~~algebra''' is a [[C-algebra]] ''A'' such that~~ the ~~injective and projective C-cross norms on ''A''⊗''B''~~ are the ~~same~~ for every ~~C-algebra ''B''~~. ~~These were first studied by {{harvtxt\|Takesaki\|1964}} under the name "Property T" (~~this ~~is unconnected with [[Kazhdan's property T]]).~~		If you are trying into a house security resolution to your house, then you will undoubtedly come across quite a lot of wi-fi dwelling safety methods amongst the entire traditional exhausting wired programs. Wireless home safety techniques are beginning to take over the home security market for a lot of causes. But not all wireless systems will be the finest resolution for every dwelling. On this information I will go over many of the pros and cons of owning a wi-fi home security system, as well as provide tips of what to look for in acquiring a very efficient setup for your scenario.<br>We do not bias our house security methods reviews to a sure firm. We analysis and analyze each safety company and their client evaluations, home alarm monitoring expertise and tools. Once now we have collected all of this information, we then examine all of the companies and determine a winner based mostly on what alarm firm has scored the best marks in each class. The whole evaluation course of takes a number of weeks to finish but ultimately we come out with the very best residence security company. This years winner was FrontPoint Safety. If you loved this informative article and you would want to receive more information regarding webpage ([http://besthomesecuritysystems.drupalgardens.com check this link right here now]) i implore you to visit our own web-site. SORTS OF RESIDENCE ALARM SYSTEMS LANDLINE DWELLING ALARM PROGRAMS<br>The wi-fi safety techniques category is our our most popular offering for do-it-yourself residence security. With the house expertise retailer's exclusive simple to learn dwelling security set up manuals and movies anybody can own a wireless security system with out paying an costly safety system installer or signing a multi-year contract. Every wireless safety system affords an array of sensors to guard your home and household. Select from Door and Window sensors, Movement Detectors, Glass break Sensors and Smoke Detectors. Our wi-fi safety techniques additionally offer you wi-fi keyfob and keypad choices giving you access to arm and disarm from a number of areas within the house.<br>As a number one supplier of Michigan residence safety systems, with the highest potential BBB score of A+ and UL permitted monitoring, Watchdog Safety takes delight in providing custom-made alarm system options that meet the unique, particular person wants of our shoppers. Our house alarm methods are by no means packaged. One in all our skilled technicians will take the time to know your particular safety wants, and construct your system from scratch to offer your loved ones with the peace of thoughts it deserves. We provide an in depth range of leading edge detection and alarm products to successfully protect any residence, large or small.<br>Inquire for a free consultation with our security camera experts who will guide you in choosing the best safety cameras that will cater to the precise surveillance and safety wants. These built-in methods may very well be synchronized with almost all cellular devices for enhanced safety and ease of entry. A purchaser can even inquire about the products and their options immediately by calling us anytime using the given telephone contact details. We take great pride in offering excellent set up providers which show you how to secure your house with great ease Stop Paying For Overpriced Security Programs with our Finest Price Assure<br>We offer you the very best worth within the business on our Complete Surveillance Methods Choose from any of our indoor and outdoor digicam CCTV kits Whether or not you select our 4 channel Surveillance System for a house security, otherwise you go additional with our 8 channel Surveillance System or sixteen channel Surveillance System for CCTV surveillance at dwelling or for small business, you'll be able to't go flawed. There are many features to think about when you're designing your CCTV dwelling security systems Our store pre-package deal in 4,8,16 channel safety system and will be configured to meet your actual CCTV safety wants.<br>The varieties of set up and sensors out there makes a distinction when selecting the perfect house safety system on your needs. As a result of threats can come from wherever in your house, search for a home safety system that protects all entrances and exits. One of the best security systems supply door and window sensors, recessed door sensors and storage door sensors. If you wish to monitor children or pets, look for companies that offer video monitoring tools to document video in your home that you would be able to entry by means of distant methods. Also, think about whether you need to install a wireless or wired system. This may make a distinction in options and worth.<br>Some homeowners might select to put in their alarm systems on their own, but with the assistance of an expert set up technician, you could be sure the system is installed correctly. Most importantly, safety programs set up by a house security firm often come with a service plan or generally even a assured warranty, which covers prices, maintenance and repairs for faulty tools. Don’t get left holding the invoice for those who arrange your personal residence safety system and then find it's important to spend further money due to incorrect wiring or improper installment. Why do I need dwelling safety?<br>This actually goes hand in hand with the perfect wi-fi dwelling alarm but there is a clear winner and it’s FrontPoint Security. While a lot of house safety firms don’t wish to trouble with renters (sorry if you're a renter nevertheless it’s true), FrontPoint Safety recognizes the importance of safety particularly for renters. In all probability among the best features of owning a house alarm system in case you stay with roommates is the ability to be alerted when somebody goes into your room. Simply place a door sensor on the door to your bedroom then configure your system to ship you a textual content message anytime it’s opened. <br>ADT House Monitoring Systems are monitored each second by educated professionals. The gear used is cutting-edge and if there is an interruption in connecting to one of the ADT monitoring centers at any second, another ADT center will take over instantly, continuing to assist defend your home. Skilled professionals continue to offer the safety and peace of mind via their advanced training of alarm monitoring systems. Our skilled professionals are dedicated to superior service and reliability, and are educated of all superior know-how associated with ADT These alarm techniques are available a variety of packages for various needs and budgets and do not require a phone line.

	~~== Characterizations ==~~
	~~Nuclearity admits~~ the ~~following equivalent characterizations:~~

	~~A C~~-~~algebra is nuclear if the identity map~~, as a ~~[[completely positive map]]~~, ~~approximately factors through matrix algebras~~. ~~Abelian C-algebras are nuclear~~. ~~One might say that nuclearity means that~~ the ~~C-algebra admits noncommutative "~~[~~[partitions of unity]~~]."
	~~A C~~-~~algebra~~ is ~~nuclear if~~ and ~~only if its enveloping [[von Neumann algebra]] is injective~~.
	~~A separable C~~-~~algebra is nuclear if~~ and ~~only if it is isomorphic~~ to a ~~C*-subalgebra ''B''~~ of the ~~[[Cuntz algebra]]~~ <~~math>\mathcal{O}_2</math~~> with the ~~property~~ that ~~there exists a [[conditional expectation]]~~ from <~~math>\mathcal{O}_2</math~~> to ~~''B''~~.

	~~==See also==~~
	*[[Nuclear space]]
	~~[[Exact C~~-~~algebra]]~~

	~~==References==~~
	*{{Citation \| last1=Connes \| first1=Alain \| author1-link=Alain Connes \| title=Classification of ~~injective factors~~. ~~\| jstor=1971057 \| mr=0454659 \| year=1976 \| journal=[[Annals~~ of ~~Mathematics\|Annals of Mathematics~~. ~~Second Series]] \| issn=0003~~-~~486X \| volume=104 \| issue=1 \| pages=73–115}}~~
	*{{Citation \| last1=Effros \| first1=Edward G. ~~\| last2=Ruan \| first2=Zhong-Jin \| title=Operator spaces \| url=http://www.oup.com/us/catalog/general/subject/Mathematics/PureMathematics/?ci=9780198534822 \| publisher=~~The ~~Clarendon Press Oxford University Press \| series=London Mathematical Society Monographs~~. ~~New Series \| isbn=978-0-19-853482-2 \| mr=1793753 \| year=2000 \| volume=23}}~~
	{{Citation \| last1=Lance \| first1=E. ~~Christopher \| title=Operator algebras~~ and ~~applications~~, ~~Part I (Kingston~~, ~~Ont~~., ~~1980) \| publisher=Amer~~. ~~Math~~. ~~Soc~~. ~~\| location=Providence~~, R.~~I. \| series=Proc. Sympos. Pure Math. \| mr=679721 \| year=1982 \| volume=38 \| chapter=Tensor products~~ and ~~nuclear C-algebras \| pages=379–399}}~~
	*{{Citation \| last1=Pisier \| first1=Gilles \| title=Introduction to ~~operator space theory \| publisher=[[Cambridge University Press]] \| series=London Mathematical Society Lecture Note Series \| isbn=978~~-~~0-521-81165-1 \| mr=2006539 \| year=2003 \| volume=294}}~~
	{{Citation \| last1=Rørdam \| first1=M. ~~\| title=Classification~~ of ~~nuclear C-algebras~~. ~~Entropy~~ in ~~operator algebras \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Encyclopaedia Math~~. ~~Sci~~. ~~\| mr=1878882 \| year=2002 \| volume=126 \| chapter=Classification~~ of ~~nuclear simple C*-algebras \| pages=1–145}}~~
	{{Citation \| last1=Takesaki \| first1=Masamichi \| title=On the ~~cross-norm of~~ the ~~direct product~~ of ~~C-algebras \| mr=0165384 \| year=1964 \| journal=The Tohoku Mathematical Journal. Second Series \| issn=0040-8735 \| volume=16 \| pages=111–122}}~~
	{{Citation \| last1=Takesaki \| first1=Masamichi \| title=Theory of ~~operator algebras~~. ~~III \| publisher=[[Springer-Verlag]] \| location=Berlin~~, ~~New York \| series=Encyclopaedia~~ of ~~Mathematical Sciences \| isbn=978~~-~~3-540-42913-5 \| mr=1943007 \| year=2003 \| volume=127 \| chapter=Nuclear C-algebras \| pages=153–204}}~~

	~~[[Category:C*-algebras]]~~

	~~[[it:C-algebra#C-algebra nucleare]]~~

en>Jheald: /* Charge conjugation */

2013-07-07T15:42:28Z

Charge conjugation

← Older revision		Revision as of 17:42, 7 July 2013
Line 1:		Line 1:
	~~Broadcast Transmitter Operator Eusebio from Moose Jaw~~, ~~usually spends time~~ with ~~hobbies for instance rock collecting~~, ~~Home Security Systems~~ and ~~kids~~. ~~Finds travel~~ a ~~fantastic experience after paying~~ a ~~visit to Kalwaria Zebrzydowska: Pilgrimage Park.~~<br><br>~~My homepage~~ ... ~~webpage ([~~http://~~besthomesecuritysystems~~.~~drupalgardens~~.com ~~simply click~~ the ~~next internet page~~])		In mathematics, a '''nuclear C-algebra''' is a [[C-algebra]] ''A'' such that the injective and projective C-cross norms on ''A''⊗''B'' are the same for every C-algebra ''B''. These were first studied by {{harvtxt\|Takesaki\|1964}} under the name "Property T" (this is unconnected with [[Kazhdan's property T]]).

			== Characterizations ==
			Nuclearity admits the following equivalent characterizations:

			A C-algebra is nuclear if the identity map, as a [[completely positive map]], approximately factors through matrix algebras. Abelian C-algebras are nuclear. One might say that nuclearity means that the C-algebra admits noncommutative "[[partitions of unity]]."
			A C-algebra is nuclear if and only if its enveloping [[von Neumann algebra]] is injective.
			A separable C-algebra is nuclear if and only if it is isomorphic to a C*-subalgebra ''B'' of the [[Cuntz algebra]] <math>\mathcal{O}_2</math> with the property that there exists a [[conditional expectation]] from <math>\mathcal{O}_2</math> to ''B''.

			==See also==
			*[[Nuclear space]]
			[[Exact C-algebra]]

			==References==
			*{{Citation \| last1=Connes \| first1=Alain \| author1-link=Alain Connes \| title=Classification of injective factors. \| jstor=1971057 \| mr=0454659 \| year=1976 \| journal=[[Annals of Mathematics\|Annals of Mathematics. Second Series]] \| issn=0003-486X \| volume=104 \| issue=1 \| pages=73–115}}
			*{{Citation \| last1=Effros \| first1=Edward G. \| last2=Ruan \| first2=Zhong-Jin \| title=Operator spaces \| url=http://www.oup.com/us/catalog/general/subject/Mathematics/PureMathematics/?ci=9780198534822 \| publisher=The Clarendon Press Oxford University Press \| series=London Mathematical Society Monographs. New Series \| isbn=978-0-19-853482-2 \| mr=1793753 \| year=2000 \| volume=23}}
			{{Citation \| last1=Lance \| first1=E. Christopher \| title=Operator algebras and applications, Part I (Kingston, Ont., 1980) \| publisher=Amer. Math. Soc. \| location=Providence, R.I. \| series=Proc. Sympos. Pure Math. \| mr=679721 \| year=1982 \| volume=38 \| chapter=Tensor products and nuclear C-algebras \| pages=379–399}}
			*{{Citation \| last1=Pisier \| first1=Gilles \| title=Introduction to operator space theory \| publisher=[[Cambridge University Press]] \| series=London Mathematical Society Lecture Note Series \| isbn=978-0-521-81165-1 \| mr=2006539 \| year=2003 \| volume=294}}
			{{Citation \| last1=Rørdam \| first1=M. \| title=Classification of nuclear C-algebras. Entropy in operator algebras \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Encyclopaedia Math. Sci. \| mr=1878882 \| year=2002 \| volume=126 \| chapter=Classification of nuclear simple C*-algebras \| pages=1–145}}
			{{Citation \| last1=Takesaki \| first1=Masamichi \| title=On the cross-norm of the direct product of C-algebras \| mr=0165384 \| year=1964 \| journal=The Tohoku Mathematical Journal. Second Series \| issn=0040-8735 \| volume=16 \| pages=111–122}}
			{{Citation \| last1=Takesaki \| first1=Masamichi \| title=Theory of operator algebras. III \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Encyclopaedia of Mathematical Sciences \| isbn=978-3-540-42913-5 \| mr=1943007 \| year=2003 \| volume=127 \| chapter=Nuclear C-algebras \| pages=153–204}}

			[[Category:C*-algebras]]

			[[it:C-algebra#C-algebra nucleare]]

en>Helpful Pixie Bot: Dated {{Merge to}}. (Build p613)

2011-07-28T14:17:05Z

Dated {{Merge to}}. (Build p613)

New page

Broadcast Transmitter Operator Eusebio from Moose Jaw, usually spends time with hobbies for instance rock collecting, Home Security Systems and kids. Finds travel a fantastic experience after paying a visit to Kalwaria Zebrzydowska: Pilgrimage Park.<br><br>My homepage ... webpage ([http://besthomesecuritysystems.drupalgardens.com simply click the next internet page])

← Older revision		Revision as of 18:35, 20 August 2014
Line 1:		Line 1:
	~~In mathematics~~, a '''nuclear C-~~algebra''' is a [[C-algebra]] ''A'' such that~~ the ~~injective and projective C-cross norms on ''A''⊗''B''~~ are the ~~same~~ for every ~~C-algebra ''B''~~. ~~These were first studied by {{harvtxt\|Takesaki\|1964}} under the name "Property T" (~~this ~~is unconnected with [[Kazhdan's property T]]).~~		If you are trying into a house security resolution to your house, then you will undoubtedly come across quite a lot of wi-fi dwelling safety methods amongst the entire traditional exhausting wired programs. Wireless home safety techniques are beginning to take over the home security market for a lot of causes. But not all wireless systems will be the finest resolution for every dwelling. On this information I will go over many of the pros and cons of owning a wi-fi home security system, as well as provide tips of what to look for in acquiring a very efficient setup for your scenario.<br>We do not bias our house security methods reviews to a sure firm. We analysis and analyze each safety company and their client evaluations, home alarm monitoring expertise and tools. Once now we have collected all of this information, we then examine all of the companies and determine a winner based mostly on what alarm firm has scored the best marks in each class. The whole evaluation course of takes a number of weeks to finish but ultimately we come out with the very best residence security company. This years winner was FrontPoint Safety. If you loved this informative article and you would want to receive more information regarding webpage ([http://besthomesecuritysystems.drupalgardens.com check this link right here now]) i implore you to visit our own web-site. SORTS OF RESIDENCE ALARM SYSTEMS LANDLINE DWELLING ALARM PROGRAMS<br>The wi-fi safety techniques category is our our most popular offering for do-it-yourself residence security. With the house expertise retailer's exclusive simple to learn dwelling security set up manuals and movies anybody can own a wireless security system with out paying an costly safety system installer or signing a multi-year contract. Every wireless safety system affords an array of sensors to guard your home and household. Select from Door and Window sensors, Movement Detectors, Glass break Sensors and Smoke Detectors. Our wi-fi safety techniques additionally offer you wi-fi keyfob and keypad choices giving you access to arm and disarm from a number of areas within the house.<br>As a number one supplier of Michigan residence safety systems, with the highest potential BBB score of A+ and UL permitted monitoring, Watchdog Safety takes delight in providing custom-made alarm system options that meet the unique, particular person wants of our shoppers. Our house alarm methods are by no means packaged. One in all our skilled technicians will take the time to know your particular safety wants, and construct your system from scratch to offer your loved ones with the peace of thoughts it deserves. We provide an in depth range of leading edge detection and alarm products to successfully protect any residence, large or small.<br>Inquire for a free consultation with our security camera experts who will guide you in choosing the best safety cameras that will cater to the precise surveillance and safety wants. These built-in methods may very well be synchronized with almost all cellular devices for enhanced safety and ease of entry. A purchaser can even inquire about the products and their options immediately by calling us anytime using the given telephone contact details. We take great pride in offering excellent set up providers which show you how to secure your house with great ease Stop Paying For Overpriced Security Programs with our Finest Price Assure<br>We offer you the very best worth within the business on our Complete Surveillance Methods Choose from any of our indoor and outdoor digicam CCTV kits Whether or not you select our 4 channel Surveillance System for a house security, otherwise you go additional with our 8 channel Surveillance System or sixteen channel Surveillance System for CCTV surveillance at dwelling or for small business, you'll be able to't go flawed. There are many features to think about when you're designing your CCTV dwelling security systems Our store pre-package deal in 4,8,16 channel safety system and will be configured to meet your actual CCTV safety wants.<br>The varieties of set up and sensors out there makes a distinction when selecting the perfect house safety system on your needs. As a result of threats can come from wherever in your house, search for a home safety system that protects all entrances and exits. One of the best security systems supply door and window sensors, recessed door sensors and storage door sensors. If you wish to monitor children or pets, look for companies that offer video monitoring tools to document video in your home that you would be able to entry by means of distant methods. Also, think about whether you need to install a wireless or wired system. This may make a distinction in options and worth.<br>Some homeowners might select to put in their alarm systems on their own, but with the assistance of an expert set up technician, you could be sure the system is installed correctly. Most importantly, safety programs set up by a house security firm often come with a service plan or generally even a assured warranty, which covers prices, maintenance and repairs for faulty tools. Don’t get left holding the invoice for those who arrange your personal residence safety system and then find it's important to spend further money due to incorrect wiring or improper installment. Why do I need dwelling safety?<br>This actually goes hand in hand with the perfect wi-fi dwelling alarm but there is a clear winner and it’s FrontPoint Security. While a lot of house safety firms don’t wish to trouble with renters (sorry if you're a renter nevertheless it’s true), FrontPoint Safety recognizes the importance of safety particularly for renters. In all probability among the best features of owning a house alarm system in case you stay with roommates is the ability to be alerted when somebody goes into your room. Simply place a door sensor on the door to your bedroom then configure your system to ship you a textual content message anytime it’s opened. <br>ADT House Monitoring Systems are monitored each second by educated professionals. The gear used is cutting-edge and if there is an interruption in connecting to one of the ADT monitoring centers at any second, another ADT center will take over instantly, continuing to assist defend your home. Skilled professionals continue to offer the safety and peace of mind via their advanced training of alarm monitoring systems. Our skilled professionals are dedicated to superior service and reliability, and are educated of all superior know-how associated with ADT These alarm techniques are available a variety of packages for various needs and budgets and do not require a phone line.

	~~== Characterizations ==~~
	~~Nuclearity admits~~ the ~~following equivalent characterizations:~~

	~~A C~~-~~algebra is nuclear if the identity map~~, as a ~~[[completely positive map]]~~, ~~approximately factors through matrix algebras~~. ~~Abelian C-algebras are nuclear~~. ~~One might say that nuclearity means that~~ the ~~C-algebra admits noncommutative "~~[~~[partitions of unity]~~]."
	~~A C~~-~~algebra~~ is ~~nuclear if~~ and ~~only if its enveloping [[von Neumann algebra]] is injective~~.
	~~A separable C~~-~~algebra is nuclear if~~ and ~~only if it is isomorphic~~ to a ~~C*-subalgebra ''B''~~ of the ~~[[Cuntz algebra]]~~ <~~math>\mathcal{O}_2</math~~> with the ~~property~~ that ~~there exists a [[conditional expectation]]~~ from <~~math>\mathcal{O}_2</math~~> to ~~''B''~~.

	~~==See also==~~
	*[[Nuclear space]]
	~~[[Exact C~~-~~algebra]]~~

	~~==References==~~
	*{{Citation \| last1=Connes \| first1=Alain \| author1-link=Alain Connes \| title=Classification of ~~injective factors~~. ~~\| jstor=1971057 \| mr=0454659 \| year=1976 \| journal=[[Annals~~ of ~~Mathematics\|Annals of Mathematics~~. ~~Second Series]] \| issn=0003~~-~~486X \| volume=104 \| issue=1 \| pages=73–115}}~~
	*{{Citation \| last1=Effros \| first1=Edward G. ~~\| last2=Ruan \| first2=Zhong-Jin \| title=Operator spaces \| url=http://www.oup.com/us/catalog/general/subject/Mathematics/PureMathematics/?ci=9780198534822 \| publisher=~~The ~~Clarendon Press Oxford University Press \| series=London Mathematical Society Monographs~~. ~~New Series \| isbn=978-0-19-853482-2 \| mr=1793753 \| year=2000 \| volume=23}}~~
	{{Citation \| last1=Lance \| first1=E. ~~Christopher \| title=Operator algebras~~ and ~~applications~~, ~~Part I (Kingston~~, ~~Ont~~., ~~1980) \| publisher=Amer~~. ~~Math~~. ~~Soc~~. ~~\| location=Providence~~, R.~~I. \| series=Proc. Sympos. Pure Math. \| mr=679721 \| year=1982 \| volume=38 \| chapter=Tensor products~~ and ~~nuclear C-algebras \| pages=379–399}}~~
	*{{Citation \| last1=Pisier \| first1=Gilles \| title=Introduction to ~~operator space theory \| publisher=[[Cambridge University Press]] \| series=London Mathematical Society Lecture Note Series \| isbn=978~~-~~0-521-81165-1 \| mr=2006539 \| year=2003 \| volume=294}}~~
	{{Citation \| last1=Rørdam \| first1=M. ~~\| title=Classification~~ of ~~nuclear C-algebras~~. ~~Entropy~~ in ~~operator algebras \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Encyclopaedia Math~~. ~~Sci~~. ~~\| mr=1878882 \| year=2002 \| volume=126 \| chapter=Classification~~ of ~~nuclear simple C*-algebras \| pages=1–145}}~~
	{{Citation \| last1=Takesaki \| first1=Masamichi \| title=On the ~~cross-norm of~~ the ~~direct product~~ of ~~C-algebras \| mr=0165384 \| year=1964 \| journal=The Tohoku Mathematical Journal. Second Series \| issn=0040-8735 \| volume=16 \| pages=111–122}}~~
	{{Citation \| last1=Takesaki \| first1=Masamichi \| title=Theory of ~~operator algebras~~. ~~III \| publisher=[[Springer-Verlag]] \| location=Berlin~~, ~~New York \| series=Encyclopaedia~~ of ~~Mathematical Sciences \| isbn=978~~-~~3-540-42913-5 \| mr=1943007 \| year=2003 \| volume=127 \| chapter=Nuclear C-algebras \| pages=153–204}}~~

	~~[[Category:C*-algebras]]~~

	~~[[it:C-algebra#C-algebra nucleare]]~~

← Older revision		Revision as of 17:42, 7 July 2013
Line 1:		Line 1:
	~~Broadcast Transmitter Operator Eusebio from Moose Jaw~~, ~~usually spends time~~ with ~~hobbies for instance rock collecting~~, ~~Home Security Systems~~ and ~~kids~~. ~~Finds travel~~ a ~~fantastic experience after paying~~ a ~~visit to Kalwaria Zebrzydowska: Pilgrimage Park.~~<br><br>~~My homepage~~ ... ~~webpage ([~~http://~~besthomesecuritysystems~~.~~drupalgardens~~.com ~~simply click~~ the ~~next internet page~~])		In mathematics, a '''nuclear C-algebra''' is a [[C-algebra]] ''A'' such that the injective and projective C-cross norms on ''A''⊗''B'' are the same for every C-algebra ''B''. These were first studied by {{harvtxt\|Takesaki\|1964}} under the name "Property T" (this is unconnected with [[Kazhdan's property T]]).

			== Characterizations ==
			Nuclearity admits the following equivalent characterizations:

			A C-algebra is nuclear if the identity map, as a [[completely positive map]], approximately factors through matrix algebras. Abelian C-algebras are nuclear. One might say that nuclearity means that the C-algebra admits noncommutative "[[partitions of unity]]."
			A C-algebra is nuclear if and only if its enveloping [[von Neumann algebra]] is injective.
			A separable C-algebra is nuclear if and only if it is isomorphic to a C*-subalgebra ''B'' of the [[Cuntz algebra]] <math>\mathcal{O}_2</math> with the property that there exists a [[conditional expectation]] from <math>\mathcal{O}_2</math> to ''B''.

			==See also==
			*[[Nuclear space]]
			[[Exact C-algebra]]

			==References==
			*{{Citation \| last1=Connes \| first1=Alain \| author1-link=Alain Connes \| title=Classification of injective factors. \| jstor=1971057 \| mr=0454659 \| year=1976 \| journal=[[Annals of Mathematics\|Annals of Mathematics. Second Series]] \| issn=0003-486X \| volume=104 \| issue=1 \| pages=73–115}}
			*{{Citation \| last1=Effros \| first1=Edward G. \| last2=Ruan \| first2=Zhong-Jin \| title=Operator spaces \| url=http://www.oup.com/us/catalog/general/subject/Mathematics/PureMathematics/?ci=9780198534822 \| publisher=The Clarendon Press Oxford University Press \| series=London Mathematical Society Monographs. New Series \| isbn=978-0-19-853482-2 \| mr=1793753 \| year=2000 \| volume=23}}
			{{Citation \| last1=Lance \| first1=E. Christopher \| title=Operator algebras and applications, Part I (Kingston, Ont., 1980) \| publisher=Amer. Math. Soc. \| location=Providence, R.I. \| series=Proc. Sympos. Pure Math. \| mr=679721 \| year=1982 \| volume=38 \| chapter=Tensor products and nuclear C-algebras \| pages=379–399}}
			*{{Citation \| last1=Pisier \| first1=Gilles \| title=Introduction to operator space theory \| publisher=[[Cambridge University Press]] \| series=London Mathematical Society Lecture Note Series \| isbn=978-0-521-81165-1 \| mr=2006539 \| year=2003 \| volume=294}}
			{{Citation \| last1=Rørdam \| first1=M. \| title=Classification of nuclear C-algebras. Entropy in operator algebras \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Encyclopaedia Math. Sci. \| mr=1878882 \| year=2002 \| volume=126 \| chapter=Classification of nuclear simple C*-algebras \| pages=1–145}}
			{{Citation \| last1=Takesaki \| first1=Masamichi \| title=On the cross-norm of the direct product of C-algebras \| mr=0165384 \| year=1964 \| journal=The Tohoku Mathematical Journal. Second Series \| issn=0040-8735 \| volume=16 \| pages=111–122}}
			{{Citation \| last1=Takesaki \| first1=Masamichi \| title=Theory of operator algebras. III \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Encyclopaedia of Mathematical Sciences \| isbn=978-3-540-42913-5 \| mr=1943007 \| year=2003 \| volume=127 \| chapter=Nuclear C-algebras \| pages=153–204}}

			[[Category:C*-algebras]]

			[[it:C-algebra#C-algebra nucleare]]

Higher-dimensional gamma matrices - Revision history

en>Headbomb: Various citation cleanup + AWB fixes, typo(s) fixed: , → , using AWB

en>Jheald: /* Charge conjugation */

en>Helpful Pixie Bot: Dated {{Merge to}}. (Build p613)