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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 bs space ： ウィキペディア英語版 bs space In the mathematical field of functional analysis, the space bs consists of all infinite sequences (''x''''i'') of real or complex numbers such that :$\backslash sup\_n\backslash left|\backslash sum\_^n\; x\_i\backslash right|$ is finite. The set of such sequences forms a normed space with the vector space operations defined componentwise, and the norm given by :$\backslash left\backslash |x\backslash right\backslash |\_\; =\; \backslash sup\_n\backslash left|\backslash sum\_^n\; x\_i\backslash right|.$ Furthermore, with respect to metric induced by this norm, ''bs'' is complete: it is a Banach space. The space of all sequences (''x''''i'') such that the series :$\backslash sum\_^\backslash infty\; x\_i$ is convergent (possibly conditionally) is denoted by ''cs''. This is a closed vector subspace of ''bs'', and so is also a Banach space with the same norm. The space ''bs'' is isometrically isomorphic to the space of bounded sequences ℓ∞ via the mapping :$T(x\_1,x\_2,\backslash dots)\; =\; (x\_1,x\_1+x\_2,x\_1+x\_2+x\_3,\backslash dots).$ Furthermore, the space of convergent sequences ''c'' is the image of ''cs'' under ''T''. ==References== * . 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「bs 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.