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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 Commutant lifting theorem ： ウィキペディア英語版 Commutant lifting theorem In operator theory, the commutant lifting theorem, due to Sz.-Nagy and Foias, is a powerful theorem used to prove several interpolation results. ==Statement== The commutant lifting theorem states that if ''T'' is a contraction on a Hilbert space ''H'', ''U'' is its minimal unitary dilation acting on some Hilbert space ''K'' (which can be shown to exist by Sz.-Nagy's dilation theorem), and ''R'' is an operator on ''H'' commuting with ''T'', then there is an operator ''S'' on ''K'' commuting with ''U'' such that :$R\; T^n\; =\; P\_H\; S\; U^n\; \backslash vert\_H\; \backslash ;\; \backslash forall\; n\; \backslash geq\; 0,$ and :$\backslash Vert\; S\; \backslash Vert\; =\; \backslash Vert\; R\; \backslash Vert.$ In other words, an operator from the commutant of ''T'' can be "lifted" to an operator in the commutant of the unitary dilation of ''T''. 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「Commutant lifting 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.