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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 Connes embedding problem ： ウィキペディア英語版 Connes embedding problem In von Neumann algebras, the Connes embedding problem or conjecture, due to Alain Connes, asks whether every type II1 factor on a separable Hilbert space can be embedded into the ultrapower of the hyperfinite type II1 factor by a free ultrafilter. The problem admits a number of equivalent formulations. ==Statement== Let $\backslash omega$ be a free ultrafilter on the natural numbers and let ''R'' be the hyperfinite type II1 factor with trace $\backslash tau$. One can construct the ultrapower $R^\backslash omega$ as follows: let $l^\backslash infty(R)=\backslash$ be the von Neumann algebra of norm-bounded sequences and let $I\_\backslash omega=\backslash \}=0\backslash \}$. The quotient $l^\backslash infty(R)/I\_\backslash omega$ turns out to be a II1 factor with trace $\backslash tau\_(x)=lim\_\backslash tau(x\_n+I\_\backslash omega)$, where $(x\_n)\_n$ is any representative sequence of $x$. Connes' Embedding Conjecture asks whether every type II1 factor on a separable Hilbert space can be embedded into some $R^\backslash omega$. The isomorphism class of $R^\backslash omega$ is independent of the ultrafilter if and only if the continuum hypothesis is true (Ge-Hadwin and Farah-Hart-Sherman), but such an embedding property does not depend on the ultrafilter because von Neumann algebras acting on separable Hilbert spaces are, roughly speaking, very small. 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「Connes embedding problem」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.