翻訳と辞書 Words near each other ・ Kadr ・ Kadra Dam ・ Kadra Yusuf ・ Kadrenci ・ Kadri ・ Kadri (name) ・ Kadri Aytaç ・ Kadri Fellahoğlu ・ Kadri Gjata ・ Kadri Gopalnath ・ Kadish Luz ・ Kadish, Iran ・ Kadisha Valley ・ Kadisiyah ・ Kadisoka ・ Kadison transitivity theorem ・ Kadison–Kastler metric ・ Kadist Art Foundation ・ Kadita ・ Kaditcha ・ Kaditshwene ・ Kaditz Lime Tree ・ Kadivar ・ Kadiwan ・ Kadiweu language ・ Kadiweu people ・ Kadiyakurichy ・ Kadiyala ・ Kadiyala Ramachandra ・ Kadiyala Venkateswara Rao Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kadison transitivity theorem ： ウィキペディア英語版 Kadison transitivity theorem In mathematics, Kadison transitivity theorem is a result in the theory of C *-algebras that, in effect, asserts the equivalence of the notions of topological irreducibility and algebraic irreducibility of representations of C *-algebras. It implies that, for irreducible representations of C *-algebras, the only non-zero linear invariant subspace is the whole space. The theorem, proved by Richard Kadison, was surprising as ''a priori'' there is no reason to believe that all topologically irreducible representations are also algebraically irreducible. ==Statement== A family $\backslash mathcal$ of bounded operators on a Hilbert space $\backslash mathcal$ is said to act ''topologically irreducibly'' when $\backslash$ and $\backslash mathcal$ are the only closed stable subspaces under $\backslash mathcal$. The family $\backslash mathcal$ is said to act ''algebraically irreducibly'' if $\backslash$ and $\backslash mathcal$ are the only linear manifolds in $\backslash mathcal$ stable under $\backslash mathcal$. Theorem. If the C *-algebra $\backslash mathfrak$ acts topologically irreducibly on the Hilbert space $\backslash mathcal,\; \backslash$ is a set of vectors and $\backslash$ is a linearly independent set of vectors in $\backslash mathcal$, there is an $A$ in $\backslash mathfrak$ such that $Ax\_j\; =\; y\_j$. If $Bx\_j\; =\; y\_j$ for some self-adjoint operator $B$, then $A$ can be chosen to be self-adjoint. Corollary. If the C *-algebra $\backslash mathfrak$ acts topologically irreducibly on the Hilbert space $\backslash mathcal$, then it acts algebraically irreducibly. 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「Kadison transitivity 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.