SOME REMARKS ON HAAGERUP'S APPROXIMATION PROPERTY

SOME REMARKS ON HAAGERUP'S APPROXIMATION PROPERTY

A finite von Neumann algebra M with a faithful normal trace τ has Haagerup's approximation property if there exists a pointwise deformation of the identity in 2-norm by subtracial compact completely positive maps. In this paper we prove that the subtraciality condition can be removed. This enab...

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Veröffentlicht in:Journal of operator theory 2011-03, Vol.65 (2), p.403-417
Hauptverfasser: BANNON, JON P., FANG, JUNSHENG
Format: Artikel
Sprache:eng
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Approximation
Coefficients
Hilbert spaces
Mathematical theorems
Mathematical vectors
Property titles
Subalgebras
Topology
Von Neumann algebra
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FANG, JUNSHENG
description A finite von Neumann algebra M with a faithful normal trace τ has Haagerup's approximation property if there exists a pointwise deformation of the identity in 2-norm by subtracial compact completely positive maps. In this paper we prove that the subtraciality condition can be removed. This enables us to provide a description of Haagerup's approximation property in terms of correspondences. We also show that if N ⊂ M is an amenable inclusion of finite von Neumann algebras and N has Haagerup's approximation property, then M also has Haagerup's approximation property.
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subjects Approximation
Coefficients
Hilbert spaces
Mathematical theorems
Mathematical vectors
Property titles
Subalgebras
Topology
Von Neumann algebra
title SOME REMARKS ON HAAGERUP'S APPROXIMATION PROPERTY
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