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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 Smith space ： ウィキペディア英語版 Smith space In functional analysis and related areas of mathematics, Smith space is a complete compactly generated locally convex space $X$ having a compact set $K$ which absorbs every other compact set $T\backslash subseteq\; X$ (i.e. $T\backslash subseteq\backslash lambda\backslash cdot\; K$ for some $\backslash lambda>0$). Smith spaces are named after M. F. Smith,〔.〕 who introduced them as duals to Banach spaces in some versions of duality theory for topological vector spaces. All Smith spaces are stereotype and are in the stereotype duality relations with Banach spaces:〔.〕〔.〕 : * for any Banach 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 Smith space, : * and vice versa, for any Smith space $X$ its stereotype dual space $X^\backslash star$ is a Banach space. == Notes == 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「Smith 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.