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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 Universal representation (C*-algebra) ： ウィキペディア英語版 Universal representation (C*-algebra) In the theory of C *-algebras, the universal representation of a C *-algebra is a faithful representation which is the direct sum of the GNS representations corresponding to the states of the C *-algebra. The various properties of the universal representation are used to obtain information about the ideals and quotients of the C *-algebra. The close relationship between an arbitrary representation of a C *-algebra and its universal representation can be exploited to obtain several criteria for determining whether a linear functional on the algebra is ultraweakly continuous. The method of using the properties of the universal representation as a tool to prove results about the C *-algebra and its representations is commonly referred to as ''universal representation techniques'' in the literature. ==Formal definition and properties== :Definition. Let ''A'' be a C *-algebra with state space ''S''. The representation ::$\backslash Phi\; :=\; \backslash sum\_\; \backslash oplus\; \backslash ;\; \backslash pi\_\backslash rho$ :on the Hilbert space $H\_$ is known as the universal representation of ''A''. As the universal representation is faithful, ''A'' is *-isomorphic to the C *-subalgebra Φ(''A'') of ''B(HΦ)''. 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「Universal representation (C*-algebra)」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.