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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 Strictly singular operator ： ウィキペディア英語版 Strictly singular operator In functional analysis, a branch of mathematics, a strictly singular operator is a bounded linear operator ''L'' from a Banach space ''X'' to another Banach space ''Y'', such that it is not an isomorphism, and fails to be an isomorphism on any infinite dimensional subspace of ''X''. Any compact operator is strictly singular, but not vice versa.〔N.L. Carothers, ''A Short Course on Banach Space Theory'', (2005) London Mathematical Society Student Texts 64, Cambridge University Press.〕〔C. J. Read, ''Strictly singular operators and the invariant subspace problem'', Studia Mathematica 132 (3) (1999), 203-226. (fulltext )〕 The class of all strictly singular operators is quite nice in the sense that it forms a norm-closed operator ideal. Every bounded linear map $T:l\_p\backslash to\; l\_q$, for , $p\backslash ne\; q$, is strictly singular. Here, $l\_p$ and $l\_q$ are sequence spaces. Similarly, every bounded linear map $T:c\_0\backslash to\; l\_p$ and $T:l\_p\backslash to\; c\_0$, for , is strictly singular. Here $c\_0$ is the Banach space of sequences converging to zero. This is a corollary of Pitt's theorem, which states that such ''T'', for ''q'' < ''p'', are compact. ==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「Strictly singular operator」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.