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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 Weak trace-class operator ： ウィキペディア英語版 In mathematics, a weak trace class operator is a compact operator on a separable Hilbert space ''H'' with singular values the same order as the harmonic sequence.When the dimension of ''H'' is infinite the ideal of weak trace-class operators has fundamentally different properties than the ideal of trace class operators. The usual operator trace on the trace-class operators does not extend to the weak trace class. Instead the ideal of weak trace-class operators admits an infinite number of linearly independent quasi-continuous traces, and it is the smallest two-sided ideal for which all traces on it are singular traces.Weak trace-class operators feature in the noncommutative geometry of French mathematician Alain Connes.== Definition ==A compact operator ''A'' on an infinite dimensional separable Hilbert space ''H'' is ''weak trace class'' if μ(''n'',''A'') O(''n''−1), where μ(''A'') is the sequence of singular values. In mathematical notation the two-sided ideal of all weak trace-class operators is denoted,:::: L_ = \. The term weak trace-class, or weak-''L''1, is used because the operator ideal corresponds, in J. W. Calkin's correspondence between two-sided ideals of bounded linear operators and rearrangement invariant sequence spaces, to the weak-''l''1 sequence space. In mathematics, a weak trace class operator is a compact operator on a separable Hilbert space ''H'' with singular values the same order as the harmonic sequence. When the dimension of ''H'' is infinite the ideal of weak trace-class operators has fundamentally different properties than the ideal of trace class operators. The usual operator trace on the trace-class operators does not extend to the weak trace class. Instead the ideal of weak trace-class operators admits an infinite number of linearly independent quasi-continuous traces, and it is the smallest two-sided ideal for which all traces on it are singular traces. Weak trace-class operators feature in the noncommutative geometry of French mathematician Alain Connes. == Definition == A compact operator ''A'' on an infinite dimensional separable Hilbert space ''H'' is ''weak trace class'' if μ(''n'',''A'') O(''n''−1), where μ(''A'') is the sequence of singular values. In mathematical notation the two-sided ideal of all weak trace-class operators is denoted, ::::$L\_\; =\; \backslash .$ The term weak trace-class, or weak-''L''1, is used because the operator ideal corresponds, in J. W. Calkin's correspondence between two-sided ideals of bounded linear operators and rearrangement invariant sequence spaces, to the weak-''l''1 sequence 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「In mathematics, a weak trace class operator is a compact operator on a separable Hilbert space ''H'' with singular values the same order as the harmonic sequence.When the dimension of ''H'' is infinite the ideal of weak trace-class operators has fundamentally different properties than the ideal of trace class operators. The usual operator trace on the trace-class operators does not extend to the weak trace class. Instead the ideal of weak trace-class operators admits an infinite number of linearly independent quasi-continuous traces, and it is the smallest two-sided ideal for which all traces on it are singular traces.Weak trace-class operators feature in the noncommutative geometry of French mathematician Alain Connes.== Definition ==A compact operator ''A'' on an infinite dimensional separable Hilbert space ''H'' is ''weak trace class'' if μ(''n'',''A'') O(''n''−1), where μ(''A'') is the sequence of singular values. In mathematical notation the two-sided ideal of all weak trace-class operators is denoted,:::: L_ = \. The term weak trace-class, or weak-''L''1, is used because the operator ideal corresponds, in J. W. Calkin's correspondence between two-sided ideals of bounded linear operators and rearrangement invariant sequence spaces, to the weak-''l''1 sequence 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.