Abstract Connes' approximate embedding problem, asks whether any countably generated type II1 II1 factor M Mcan be approximately embedded in the hyperfinite type II1 factor. Solving this problem in the affirmative, amounts to showing that given any integers N,p , any elements x1,…,xN in Mand any ϵ>0 one can find k and matrices X1,…,XN in the algebra Mk(ℂ), endowed with the normalized trace \ tr , such that for every i1,…,ip∈{1,…,N} and for every s with 1≤s≤p s that |τ(xi1…xis)−\ tr\ (Xi1…Xis)|<ϵ. In this paper we show that this is always possible if s s is 2 and 3.

Radulescu, F. (1999). Convex sets associated with von~Neumann algebras and Connes' approximate embedding problem. MATHEMATICAL RESEARCH LETTERS, 6(2), 229-236 [10.4310/MRL.1999.v6.n2.a11].

Convex sets associated with von~Neumann algebras and Connes' approximate embedding problem

RADULESCU, FLORIN
1999

Abstract

Abstract Connes' approximate embedding problem, asks whether any countably generated type II1 II1 factor M Mcan be approximately embedded in the hyperfinite type II1 factor. Solving this problem in the affirmative, amounts to showing that given any integers N,p , any elements x1,…,xN in Mand any ϵ>0 one can find k and matrices X1,…,XN in the algebra Mk(ℂ), endowed with the normalized trace \ tr , such that for every i1,…,ip∈{1,…,N} and for every s with 1≤s≤p s that |τ(xi1…xis)−\ tr\ (Xi1…Xis)|<ϵ. In this paper we show that this is always possible if s s is 2 and 3.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
English
Connes embedding conjecture
Radulescu, F. (1999). Convex sets associated with von~Neumann algebras and Connes' approximate embedding problem. MATHEMATICAL RESEARCH LETTERS, 6(2), 229-236 [10.4310/MRL.1999.v6.n2.a11].
Radulescu, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/171348
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