Symmetrizable compact operator - Revision history

en>Michael Hardy at 04:10, 30 July 2014

2014-07-30T04:10:51Z

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-==Definition==
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-A [[C*-algebra]] ''E'' is exact if, for any [[short exact sequence]],
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-:<math>0 \;\xrightarrow{}\; A \;\xrightarrow{f}\; B \;\xrightarrow{g}\; C \;\xrightarrow{}\; 0</math>
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en>Orenburg1: sp

2013-07-06T09:13:51Z

← Older revision		Revision as of 11:13, 6 July 2013
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	~~However~~, ~~one takes~~ a ~~lot of care and planning while detailing to make this occasion grandeur.<br>When I got on~~ the ~~bus, the girls seemed to look at me differently~~. ~~I thought maybe it was my confidence~~, ~~but then I thought who the heck cares~~, ~~they were looking at me! So I looked back at them and they giggled.~~<br>~~http://greentreetearoom.com/fashion/?p=175~~ <br /> ~~http~~://~~greentreetearoom~~.~~com/fashion/?p~~=~~471 <br /> http~~:~~//greentreetearoom~~.~~com/fashion/?p=76~~ <~~br /~~> ~~http://greentreetearoom.com/fashion/?p=651~~ <br /> ~~http://greentreetearoom~~.~~com/fashion/?p~~=~~571~~ <~~br /> <br>~~http://~~math-preview~~.~~wmflabs~~.org/wiki/~~9_Secrets_About_Bags_Outlet_They_Are_Still_Keeping_From_You<br>http~~:~~//vetopia~~.~~dothome~~.~~co.kr/xe/?document_srl~~=~~1354604<br><br>If you liked this article~~ and ~~you simply would like to obtain more info regarding~~ [~~http~~:~~//www.restaurantcalcuta.com/outlet/ugg.asp Uggs Outlet Online~~] ~~please visit the web-site.~~		{{DISPLAYTITLE:Exact C*-algebra}}

			In mathematics, an '''exact C-algebra''' is a [[C-algebra]] that preserves [[exact sequence]]s under the [[minimum tensor product]].

			==Definition==

			A [[C*-algebra]] ''E'' is exact if, for any [[short exact sequence]],

			:<math>0 \;\xrightarrow{}\; A \;\xrightarrow{f}\; B \;\xrightarrow{g}\; C \;\xrightarrow{}\; 0</math>

			the sequence

			:<math>0\;\xrightarrow{}\; A \otimes_\min E\;\xrightarrow{f\otimes \operatorname{id}}\; B\otimes_\min E \;\xrightarrow{g\otimes \operatorname{id}}\; C\otimes_\min E \;\xrightarrow{}\; 0,</math>

			where &otimes;<sub>min</sub> denotes the minimum [[tensor product]], is also exact.

			==Properties==

			Exact C*-algebras have the following equivalent characterizations:

			A C-algebra ''A'' is exact if and only if ''A'' is nuclearly embeddable into ''B''(''H''), the C*-algebra of all bounded operators on a Hilbert space ''H''.
			A separable C-algebra ''A'' is exact if and only if it is isomorphic to a subalgebra of the [[Cuntz algebra]] <math>\mathcal{O}_2</math>.

			All [[nuclear C-algebra]]s and their C-subalgebras are exact.

			==References==
			{{reflist}}
			<!--- After listing your sources please cite them using inline citations and place them after the information they cite. Please see http://en.wikipedia.org/wiki/Wikipedia:REFB for instructions on how to add citations. --->
			*{{cite book
			\|first1=Nathanial P.
			\|last1=Brown
			\|first2=Narutaka
			\|last2=Ozawa
			\|title=C*-algebras and Finite-Dimensional Approximations
			\|publisher=AMS
			\|location=Providence
			\|year=2008
			\|isbn=978-0-8218-4381-9
			}}
			*
			*
			*

			[[Category:C*-algebras]]

en>Mathsci: /* Discussion */

2012-08-23T14:20:44Z

Discussion

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