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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 stereotype space ： ウィキペディア英語版 stereotype space In functional analysis and related areas of mathematics stereotype spaces are topological vector spaces defined by a special variant of reflexivity condition. They form a class of spaces with a series of remarkable properties, in particular, this class is very wide (for instance, it contains all Fréchet spaces and thus, all Banach spaces), it consists of spaces satisfying a natural condition of completeness, and it forms a closed monoidal category with the standard analytical tools for constructing new spaces, like taking closed subspace, quotient space, projective and injective limits, the space of operators, tensor products, etc. ==Definition== A stereotype space〔.〕 is a topological vector space $X$ over the field $\backslash mathbb$ of complex numbers〔...or over the field $\backslash mathbb$ of real numbers, with the similar definition.〕 such that the natural map into the second dual space :$i:X\backslash to\; X^,\backslash quad\; i(x)(f)=f(x),\backslash quad\; x\backslash in\; X,\backslash quad\; f\backslash in\; X^\backslash star$ is an isomorphism of topological vector spaces (i.e. a linear and a homeomorphic map). Here the ''dual space'' $X^\backslash star$ is defined as the space of all linear continuous functionals $f:X\backslash to\backslash mathbb$ endowed with the topology of uniform convergence on totally bounded sets in ''X'', and the ''second dual space'' $X^$ is the space dual to $X^$ in the same sense. The following criterion holds:〔 a topological vector space $X$ is stereotype if and only if it is locally convex and satisfies the following two conditions: : * ''pseudocompleteness'': each totally bounded Cauchy net in $X$ converges, : * : * ''pesudosaturateness'': each closed convex balanced ''capacious''〔A set $D\backslash subseteq\; X$ is said to be ''capacious'' if for each totally bounded set $A\backslash subseteq\; X$ there is a finite set $F\backslash subseteq\; X$ such that $A\backslash subseteq\; D+F$.〕 set $D$ in $X$ is a neighborhood of zero in $X$. The property of being pseudocomplete is a weakening of the usual notion of completeness, while the property of being pseudosaturated is a weakening of the notion of barreledness of a topological vector space. 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「stereotype 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.