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In operator algebras, the enveloping von Neumann algebra of a C *-algebra is a von Neumann algebra that contains all the operator-algebraic information about the given C *-algebra. This may also be called the ''universal'' enveloping von Neumann algebra, since it is given by a universal property; and (as always with von Neumann algebras) the term ''W *-algebra'' may be used in place of ''von Neumann algebra''. == Definition == Let ''A'' be a C *-algebra and ''π''''U'' be its universal representation, acting on Hilbert space ''H''''U''. The image of ''π''''U'', ''π''''U''(''A''), is a C *-subalgebra of bounded operators on ''H''''U''. The enveloping von Neumann algebra of ''A'' is the closure of ''π''''U''(''A'') in the weak operator topology. It is sometimes denoted by ''A''′′. 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「Enveloping von Neumann algebra」の詳細全文を読む スポンサード リンク
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