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en>Fylbecatulous: Undid revision 638211404 by 150.129.102.149 (talk) sandbox / experimental edit

2014-12-15T15:31:33Z

Undid revision 638211404 by 150.129.102.149 (talk) sandbox / experimental edit

← Older revision		Revision as of 17:31, 15 December 2014
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	~~A '''uniform algebra''' ''A'' on~~ a ~~[[compact space\|compact]] [[Hausdorff space \|Hausdorff]] [[topological space]] ''X'~~' is a closed (with respect to the [[uniform norm]]) [[algebra over a field\|subalgebra]] of the [[C*-algebra]] ''C(X)'' (the continuous complex valued functions on ''X'') with the following properties:		Hi there, I am Alyson Pomerleau and I think it sounds quite good when you say it. For a while I've been in Mississippi but now I'm considering other options. The preferred hobby for him and his kids is to perform lacross and he would never give it up. He is an information officer.<br><br>Feel free to visit my web-site :: real psychic; [http://www.prograd.uff.br/novo/facts-about-growing-greater-organic-garden www.prograd.uff.br],
	~~:the constant functions are contained~~ in '~~'A''~~
	: for ~~every ''x'', ''y'' <math>\in</math> ''X'' there~~ is ~~f<math>\in</math>''A'' with f(x)<math>\ne</math>f(y). This is called separating the points of ''X''.~~

	~~As a closed subalgebra of the [[commutative]] [[Banach algebra]] ''C(X)'' a uniform algebra is itself a unital commutative Banach algebra (when equipped with the uniform norm). Hence,~~ it ~~is, (by definition) a [[Banach function algebra]]~~.

	~~A uniform algebra ''A'' on ''X''~~ is ~~said to be '''natural''' if the [[maximal ideal]]s of ''A'' precisely are the ideals <math>M_x</math> of functions vanishing at a point ''x'' in ''X''~~.

	~~==Abstract characterization==~~
	~~If ''A'' is a [[unital algebra\|unital]] [[commutative]] [[Banach algebra]] such that~~ <~~math~~>~~\|\|a^2\|\| = \|\|a\|\|^2~~<~~/math~~> ~~for all ''a'' in ''A'', then there is a [[compact space\|compact]] [[Hausdorff space \|Hausdorff]] ''X'' such that ''A'' is isomorphic as a Banach algebra~~ to ~~a uniform algebra on ''X''. This result follows from the spectral radius formula and the Gelfand representation.~~

	~~{{mathanalysis~~-~~stub}}~~

	~~[[Category~~:~~Functional analysis]]~~

	[[~~Category~~:~~Banach algebras]~~]

en>ChrisGualtieri: Remove stub template(s). Page is start class or higher. Also check for and do General Fixes + Checkwiki fixes using AWB

2013-12-13T16:56:43Z

Remove stub template(s). Page is start class or higher. Also check for and do General Fixes + Checkwiki fixes using AWB

← Older revision		Revision as of 18:56, 13 December 2013
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	~~The author~~'~~s name~~ is ~~Christy. I~~'~~ve always cherished residing~~ in ~~Kentucky but now I~~'~~m considering other options~~. ~~Invoicing~~ is ~~my profession~~. ~~One~~ of the ~~extremely very best issues in~~ the ~~world for him~~ is ~~performing ballet and he~~'ll be ~~starting some thing else along with it~~.<br><br>~~Here~~ is ~~my homepage~~ ..~~. authentic psychic readings (~~[~~http~~:~~//www.sirudang.com/siroo_Notice/2110 sirudang.com~~])		A '''uniform algebra''' ''A'' on a [[compact space\|compact]] [[Hausdorff space \|Hausdorff]] [[topological space]] ''X'' is a closed (with respect to the [[uniform norm]]) [[algebra over a field\|subalgebra]] of the [[C*-algebra]] ''C(X)'' (the continuous complex valued functions on ''X'') with the following properties:
			:the constant functions are contained in ''A''
			: for every ''x'', ''y'' <math>\in</math> ''X'' there is f<math>\in</math>''A'' with f(x)<math>\ne</math>f(y). This is called separating the points of ''X''.

			As a closed subalgebra of the [[commutative]] [[Banach algebra]] ''C(X)'' a uniform algebra is itself a unital commutative Banach algebra (when equipped with the uniform norm). Hence, it is, (by definition) a [[Banach function algebra]].

			A uniform algebra ''A'' on ''X'' is said to be '''natural''' if the [[maximal ideal]]s of ''A'' precisely are the ideals <math>M_x</math> of functions vanishing at a point ''x'' in ''X''.

			==Abstract characterization==
			If ''A'' is a [[unital algebra\|unital]] [[commutative]] [[Banach algebra]] such that <math>\|\|a^2\|\| = \|\|a\|\|^2</math> for all ''a'' in ''A'', then there is a [[compact space\|compact]] [[Hausdorff space \|Hausdorff]] ''X'' such that ''A'' is isomorphic as a Banach algebra to a uniform algebra on ''X''. This result follows from the spectral radius formula and the Gelfand representation.

			{{mathanalysis-stub}}

			[[Category:Functional analysis]]

			[[Category:Banach algebras]]

114.108.192.20: /* Implementation */

2012-08-15T01:16:53Z

Implementation

New page

The author's name is Christy. I've always cherished residing in Kentucky but now I'm considering other options. Invoicing is my profession. One of the extremely very best issues in the world for him is performing ballet and he'll be starting some thing else along with it.<br><br>Here is my homepage ... authentic psychic readings ([http://www.sirudang.com/siroo_Notice/2110 sirudang.com])