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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 Completely positive map ： ウィキペディア英語版 Completely positive map In mathematics a positive map is a map between C *-algebras that sends positive elements to positive elements. A completely positive map is one which satisfies a stronger, more robust condition. == Definition == Let $A$ and $B$ be C *-algebras. A linear map $\backslash phi:\; A\backslash to\; B$ is called positive map if $\backslash phi$ maps positive elements to positive elements: $a\backslash geq\; 0\; \backslash implies\; \backslash phi(a)\backslash geq\; 0$. Any linear map $\backslash phi:A\backslash to\; B$ induces another map :$\backslash textrm\; \backslash otimes\; \backslash phi\; :\; \backslash mathbb^\; \backslash otimes\; A\; \backslash to\; \backslash mathbb^\; \backslash otimes\; B$ in a natural way. If $\backslash mathbb^\backslash otimes\; A$ is identified with the C *-algebra $A^$ of $k\backslash times\; k$-matrices with entries in $A$, then $\backslash textrm\backslash otimes\backslash phi$ acts as :$$ \begin a_ & \cdots & a_ \\ \vdots & \ddots & \vdots \\ a_ & \cdots & a_ \end \mapsto \begin \phi(a_) & \cdots & \phi(a_) \\ \vdots & \ddots & \vdots \\ \phi(a_) & \cdots & \phi(a_) \end. We say that $\backslash phi$ is k-positive if $\backslash textrm\_\}\; \backslash otimes\; \backslash Phi$ is a positive map, and $\backslash phi$ is called completely positive if $\backslash phi$ is k-positive for all k. 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「Completely positive map」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.