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In the mathematical field of functional analysis, the space bs consists of all infinite sequences (''x''''i'') of real or complex numbers such that : is finite. The set of such sequences forms a normed space with the vector space operations defined componentwise, and the norm given by : 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 : 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 : 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
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