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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 Shilov boundary ： ウィキペディア英語版 Shilov boundary In functional analysis, a branch of mathematics, the Shilov boundary is the smallest closed subset of the structure space of a commutative Banach algebra where an analog of the maximum modulus principle holds. It is named after its discoverer, Georgii Evgen'evich Shilov. == Precise definition and existence == Let $\backslash mathcal\; A$ be a commutative Banach algebra and let $\backslash Delta\; \backslash mathcal\; A$ be its structure space equipped with the relative weak *-topology of the dual $^$ *. A closed (in this topology) subset $F$ of $\backslash Delta$ is called a boundary of $$ if $\backslash max\_\; |x(f)|$ for all $x\; \backslash in\; \backslash mathcal\; A$. The set $S=\backslash bigcap\backslash \backslash \}$ is called the Shilov boundary. It has been proved by Shilov〔Theorem 4.15.4 in Einar Hille, Ralph S. Phillips: (Functional analysis and semigroups ). -- AMS, Providence 1957.〕 that $S$ is a boundary of $$. Thus one may also say that Shilov boundary is the unique set $S\; \backslash subset\; \backslash Delta\; \backslash mathcal\; A$ which satisfies #$S$ is a boundary of $\backslash mathcal\; A$, and #whenever $F$ is a boundary of $\backslash mathcal\; A$, then $S\; \backslash subset\; F$. 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「Shilov boundary」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.