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en>Kodiologist: Combined hatnotes.

2014-09-11T15:54:50Z

Combined hatnotes.

← Older revision		Revision as of 17:54, 11 September 2014
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	~~In [[functional analysis]], a branch of mathematics, the '''Ryll-Nardzewski fixed-point theorem''' states that if <math>E</math>~~ is ~~a [[normed vector space]] and <math>K</math> is a nonempty [[Convex set\|convex]] subset of <math>E</math> which is [[compact space\|compact]] under~~ the ~~[[weak topology]], then every [[group (mathematics)\|group]] (or equivalently: every [[semigroup]])~~ of ~~[[affine map\|affine]] [[isometry\|isometries]] of <math>K</math> has at least one fixed point~~. ~~(Here, a ''fixed point''~~ of ~~a set of maps~~ is ~~a point that~~ is ~~[[Fixed point (mathematics)\|fixed]] by each map in the set~~.)		She is recognized by the name of Myrtle Shryock. One of the things he enjoys most is ice skating but he is having difficulties to discover time for it. Years ago he moved to North Dakota and his family members enjoys it. She is a librarian but she's usually wanted her own business.<br><br>Look into my webpage ... [http://www.siccus.net/blog/15356 std testing at home]

	~~This theorem was announced by [[Czesław Ryll-Nardzewski]].<ref>{{cite journal\|first=C.\|last=Ryll-Nardzewski\|title=Generalized random ergodic theorems~~ and ~~weakly almost periodic functions\|journal=Bull~~. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.\|volume=10\|year=1962\|pages=271–275}}</ref> Later Namioka and Asplund <ref>{{cite journal\|doi=10.1090/S0002-9904-1967-11779-8\|first=I.\|last=Namioka\|coauthors=Asplund, E.\|title=A geometric proof of Ryll-Nardzewski's ~~fixed point theorem\|journal=Bull. Amer. Math. Soc~~.~~\|volume=73\|issue=3\|year=1967\|pages=443–445}}~~<~~/ref~~> ~~gave a proof based on a different approach. Ryll-Nardzewski himself gave a complete proof in the original spirit.~~<~~ref~~>~~{{cite journal\|first=C.\|last=Ryll-Nardzewski\|title=On fixed points of semi-groups of endomorphisms of linear spaces\|journal=Proc~~. ~~5-th Berkeley Symp~~. ~~Probab~~. ~~Math. Stat\|volume=2: 1\|publisher=Univ. California Press\|year=1967\|pages=55–61}}</ref>~~

	~~==Applications==~~
	The Ryll-Nardzewski theorem yields the existence of a [[Haar measure]] on compact groups.<ref>{{cite book\|first=N.\|last=Bourbaki\|title=Espaces vectoriels topologiques. Chapitres 1 à 5\|series=Éléments de mathématique.\|edition=New\|publisher=Masson\|location=Paris\|year=1981\|isbn=2-225-68410-3}}</ref><!-- there seems to be a gap in the approach described in Conway's "A Course in Functional Analysis", about the treatment of weak vs. weak* topology -->

	~~==See also==~~
	* [[Fixed-point theorem]]s
	* [[Fixed-point theorems in infinite-dimensional spaces]]

	~~==References==~~
	~~<references />~~
	* Andrzej Granas and [[James Dugundji]], ''Fixed Point Theory'' (2003) Springer-Verlag, New York, ISBN 0-387-00173-5.
	* [http://www.~~math~~.~~harvard.edu~~/~~~lurie~~/~~261ynotes/lecture26.pdf A proof written by J. Lurie]~~

	~~[[Category:Fixed points (mathematics)]]~~
	~~[[Category:Functional analysis]]~~
	~~[[Category:Theorems in functional analysis]~~]

en>R'n'B: Fix links to disambiguation page Ordinal

2013-04-10T17:41:00Z

Fix links to disambiguation page Ordinal

← Older revision		Revision as of 19:41, 10 April 2013
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	~~Hi there~~, ~~I am Sophia. The preferred hobby for him~~ and ~~his children~~ is ~~style and he'll be starting something else along with it. Invoicing~~ is ~~my occupation~~. ~~For many years she~~'~~s been living~~ in ~~Kentucky but her husband wants them to transfer~~.<br><br>~~Here is my web blog psychic readers; [http:~~//~~www~~.~~article~~-~~galaxy~~.~~com~~/~~profile~~.~~php?~~a=~~143251~~ http://www.~~article-galaxy~~.~~com~~/],		In [[functional analysis]], a branch of mathematics, the '''Ryll-Nardzewski fixed-point theorem''' states that if <math>E</math> is a [[normed vector space]] and <math>K</math> is a nonempty [[Convex set\|convex]] subset of <math>E</math> which is [[compact space\|compact]] under the [[weak topology]], then every [[group (mathematics)\|group]] (or equivalently: every [[semigroup]]) of [[affine map\|affine]] [[isometry\|isometries]] of <math>K</math> has at least one fixed point. (Here, a ''fixed point'' of a set of maps is a point that is [[Fixed point (mathematics)\|fixed]] by each map in the set.)

			This theorem was announced by [[Czesław Ryll-Nardzewski]].<ref>{{cite journal\|first=C.\|last=Ryll-Nardzewski\|title=Generalized random ergodic theorems and weakly almost periodic functions\|journal=Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.\|volume=10\|year=1962\|pages=271–275}}</ref> Later Namioka and Asplund <ref>{{cite journal\|doi=10.1090/S0002-9904-1967-11779-8\|first=I.\|last=Namioka\|coauthors=Asplund, E.\|title=A geometric proof of Ryll-Nardzewski's fixed point theorem\|journal=Bull. Amer. Math. Soc.\|volume=73\|issue=3\|year=1967\|pages=443–445}}</ref> gave a proof based on a different approach. Ryll-Nardzewski himself gave a complete proof in the original spirit.<ref>{{cite journal\|first=C.\|last=Ryll-Nardzewski\|title=On fixed points of semi-groups of endomorphisms of linear spaces\|journal=Proc. 5-th Berkeley Symp. Probab. Math. Stat\|volume=2: 1\|publisher=Univ. California Press\|year=1967\|pages=55–61}}</ref>

			==Applications==
			The Ryll-Nardzewski theorem yields the existence of a [[Haar measure]] on compact groups.<ref>{{cite book\|first=N.\|last=Bourbaki\|title=Espaces vectoriels topologiques. Chapitres 1 à 5\|series=Éléments de mathématique.\|edition=New\|publisher=Masson\|location=Paris\|year=1981\|isbn=2-225-68410-3}}</ref><!-- there seems to be a gap in the approach described in Conway's "A Course in Functional Analysis", about the treatment of weak vs. weak* topology -->

			==See also==
			* [[Fixed-point theorem]]s
			* [[Fixed-point theorems in infinite-dimensional spaces]]

			==References==
			<references />
			* Andrzej Granas and [[James Dugundji]], ''Fixed Point Theory'' (2003) Springer-Verlag, New York, ISBN 0-387-00173-5.
			* [http://www.math.harvard.edu/~lurie/261ynotes/lecture26.pdf A proof written by J. Lurie]

			[[Category:Fixed points (mathematics)]]
			[[Category:Functional analysis]]
			[[Category:Theorems in functional analysis]]

75.32.107.34 at 05:08, 27 October 2010

2010-10-27T05:08:27Z

New page

Hi there, I am Sophia. The preferred hobby for him and his children is style and he'll be starting something else along with it. Invoicing is my occupation. For many years she's been living in Kentucky but her husband wants them to transfer.<br><br>Here is my web blog psychic readers; [http://www.article-galaxy.com/profile.php?a=143251 http://www.article-galaxy.com/],