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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 Brauner space ： ウィキペディア英語版 Brauner space In functional analysis and related areas of mathematics Brauner space is a complete compactly generated locally convex space $X$ having a sequence of compact sets $K\_n$ such that every other compact set $T\backslash subseteq\; X$ is contained in some $K\_n$. Brauner spaces are named after Kalman Brauner,〔.〕 who first started to study them. All Brauner spaces are stereotype and are in the stereotype duality relations with Fréchet spaces:〔.〕〔.〕 : * for any Fréchet space $X$ its stereotype dual space〔The ''stereotype dual'' space to a locally convex space $X$ is the space $X^\backslash star$ of all linear continuous functionals $f:X\backslash to\backslash mathbb$ endowed with the topology of uniform convergence on totally bounded sets in $X$.〕 $X^\backslash star$ is a Brauner space, : * and vice versa, for any Brauner space $X$ its stereotype dual space $X^\backslash star$ is a Fréchet space. == Examples == * Let $M$ be a $\backslash sigma$-compact locally compact topological space, and $(M)$ the space of all functions on $M$ (with values in $$ or $$), endowed with the usual topology of uniform convergence on compact sets in $M$. The dual space $^\backslash star(M)$ of measures with compact support in $M$ with the topology of uniform convergence on compact sets in $(M)$ is a Brauner space. * Let $M$ be a smooth manifold, and $(M)$ the space of smooth functions on $M$ (with values in $$ or $$), endowed with the usual topology of uniform convergence with each derivative on compact sets in $M$. The dual space $^\backslash star(M)$ of distributions with compact support in $M$ with the topology of uniform convergence on bounded sets in $(M)$ is a Brauner space. * Let $M$ be a Stein manifold and $(M)$ the space of holomorphic functions on $M$ with the usual topology of uniform convergence on compact sets in $M$. The dual space $^\backslash star(M)$ of analytic functionals on $M$ with the topology of uniform convergence on biunded sets in $(M)$ is a Brauner space. * Let $G$ be a compactly generated Stein group. The space $\_(G)$ of holomorphic functions of exponential type on $G$ is a Brauner space with respect to a natural topology.〔S.S.Akbarov, 2009.〕 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「Brauner space」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.