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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Banach function algebra ： ウィキペディア英語版 Banach function algebra In functional analysis a Banach function algebra on a compact Hausdorff space ''X'' is unital subalgebra, ''A'' of the commutative C *-algebra ''C(X)'' of all continuous, complex valued functions from ''X'', together with a norm on ''A'' which makes it a Banach algebra. A function algebra is said to vanish at a point p if f(p) = 0 for all $(f\backslash in\; A)$. A function algebra separates points if for each distinct pair of points $(p,q\; \backslash in\; X)$, there is a function $(f\backslash in\; A)$ such that $f(p)\; \backslash neq\; f(q)$. For every $x\backslash in\; X$ define $\backslash varepsilon\_x(f)=f(x)\backslash \; (f\backslash in\; A)$. Then $\backslash varepsilon\_x$ is a non-zero homomorphism (character) on $A$. Theorem: A Banach function algebra is semisimple (that is its Jacobson radical is equal to zero) and each commutative unital, semisimple Banach algebra is isomorphic (via the Gelfand transform) to a Banach function algebra on its character space (the space of algebra homomorphisms from ''A'' into the complex numbers given the relative weak * topology). If the norm on $A$ is the uniform norm (or sup-norm) on $X$, then $A$ is called a uniform algebra. Uniform algebras are an important special case of Banach function algebras. ==References== * H.G. Dales ''Banach algebras and automatic continuity'' 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Banach function algebra」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.