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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 Operator ideal ： ウィキペディア英語版 Operator ideal In functional analysis, a branch of mathematics, an operator ideal is a special kind of class of continuous linear operators between Banach spaces. If an operator $T$ belongs to an operator ideal $\backslash mathcal$, then for any operators $A$ and $B$ which can be composed with $T$ as $BTA$, then $BTA$ is class $\backslash mathcal$ as well. Additionally, in order for $\backslash mathcal$ to be an operator ideal, it must contain the class of all finite-rank Banach space operators. ==Formal definition== Let $\backslash mathcal$ denote the class of continuous linear operators acting between two Banach spaces. For any subclass $\backslash mathcal$ of $\backslash mathcal$ and any two Banach spaces $X$ and $Y$ over the same field $\backslash mathbb$, denote by $\backslash mathcal(X,Y)$ the set of continuous linear operators of the form $T:X\backslash to\; Y$. In this case, we say that $\backslash mathcal(X,Y)$ is a component of $\backslash mathcal$. An operator ideal is a subclass $\backslash mathcal$ of $\backslash mathcal$, containing every identity operator acting on a 1-dimensional Banach space, such that for any two Banach spaces $X$ and $Y$ over the same field $\backslash mathbb$, the following two conditions for $\backslash mathcal(X,Y)$ are satisfied: (1) If $S,T\backslash in\backslash mathcal(X,Y)$ then $S+T\backslash in\backslash mathcal(X,Y)$; and (2) if $W$ and $Z$ are Banach spaces over $\backslash mathbb$ with $A\backslash in\backslash mathcal(W,X)$ and $B\backslash in\backslash mathcal(Y,Z)$, and if $T\backslash in\backslash mathcal(X,Y)$, then $BTA\backslash in\backslash mathcal(W,Z)$. 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「Operator ideal」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.