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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 Dunford–Schwartz theorem ： ウィキペディア英語版 Dunford–Schwartz theorem In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz states that the averages of powers of certain norm-bounded operators on ''L''1 converge in a suitable sense.〔.〕 ==Statement of the theorem== $\backslash textT\; \backslash textL^1\; \backslash textL^1\; \backslash text\backslash |T\backslash |\_1\backslash leq\; 1\backslash text\backslash |T\backslash |\_\backslash infty\backslash leq\; 1\; \backslash text$ : $\backslash lim\_\backslash frac\backslash sum\_^T^kf$ $\backslash textf\backslash in\; L^1\backslash text$ The statement is no longer true when the boundedness condition is relaxed to even $\backslash |T\backslash |\_\backslash infty\backslash le\; 1+\backslash varepsilon$.〔.〕 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「Dunford–Schwartz theorem」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.