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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 topologies ： ウィキペディア英語版 Operator topologies In the mathematical field of functional analysis there are several standard topologies which are given to the algebra ''B''(''H'') of bounded linear operators on a Hilbert space ''H''. ==Introduction== Let be a sequence of linear operators on the Hilbert space ''H''. Consider the statement that ''T''''n'' converges to some operator ''T'' in ''H''. This could have several different meanings: * If $\backslash |T\_n\; -\; T\backslash |\; \backslash to\; 0$, that is, the operator norm of ''T''''n'' - ''T'' (the supremum of $\backslash Vert\; T\_n\; x\; -\; T\; x\; \backslash Vert\_H$, where ''x'' ranges over the unit ball in ''H'') converges to 0, we say that $T\_n\; \backslash to\; T$ in the uniform operator topology. * If $T\_n\; x\; \backslash to\; Tx$ for all ''x'' in ''H'', then we say $T\_n\; \backslash to\; T$ in the strong operator topology. * Finally, suppose $T\_n\; x\; \backslash to\; Tx$ in the weak topology of ''H''. This means that $F(T\_n\; x)\; \backslash to\; F(T\; x)$ for all linear functionals ''F'' on ''H''. In this case we say that $T\_n\; \backslash to\; T$ in the weak operator topology. All of these notions make sense and are useful for a Banach space in place of the Hilbert space ''H''. 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 topologies」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.