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arXiv:1404.6214 [math.OA]AbstractReferencesReviewsResources

The Haagerup approximation property for von Neumann algebras via quantum Markov semigroups and Dirichlet forms

Martijn Caspers, Adam Skalski

Published 2014-04-24, updated 2014-09-12Version 2

The Haagerup approximation property for a von Neumann algebra equipped with a faithful normal state $\varphi$ is shown to imply existence of unital, $\varphi$-preserving and KMS-symmetric approximating maps. This is used to obtain a characterisation of the Haagerup approximation property via quantum Markov semigroups (extending the tracial case result due to Jolissaint and Martin) and further via quantum Dirichlet forms.

Comments: 25 pages; v2 adds an example, corrects a few minor points and updates references. The article will appear in the Communications in Mathematical Physics
Categories: math.OA
Subjects: 46L10, 46L55
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