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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 Schatten class operator ： ウィキペディア英語版 Schatten class operator In mathematics, specifically functional analysis, a ''p''th Schatten-class operator is a bounded linear operator on a Hilbert space with finite ''p''th Schatten norm. The space of ''p''th Schatten-class operators is a Banach space with respect to the Schatten norm. Via polar decomposition, one can prove that the space of ''p''th Schatten class operators is an ideal in ''B(H)''. Furthermore, the Schatten norm satisfies a type of Hölder inequality: : $\backslash |\; S\; T\backslash |\; \_\; \backslash leq\; \backslash |\; S\backslash |\; \_\; \backslash |\; T\backslash |\; \_\; \backslash \; \backslash mbox\; \backslash \; S\; \backslash in\; S\_p\; ,\; \backslash \; T\backslash in\; S\_q\; \backslash mbox\; 1/p+1/q=1.$ If we denote by $S\_\backslash infty$ the Banach space of compact operators on ''H'' with respect to the operator norm, the above Hölder-type inequality even holds for $p\; \backslash in\; ()$. From this it follows that $\backslash phi\; :\; S\_p\; \backslash rightarrow\; S\_q\; \text{'}$, $T\; \backslash mapsto\; \backslash mathrm(T\backslash cdot\; )$ is a well-defined contraction. (Here the prime denotes (topological) dual.) Observe that the ''2''nd Schatten class is in fact the Hilbert space of Hilbert–Schmidt operators. Moreover, the ''1''st Schatten class is the space of trace class operators. 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「Schatten class 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.