The Haagerup approximation property for von Neumann algebras via quantum Markov semigroups and Dirichlet forms
Operator Algebras
2015-06-19 v3
Abstract
The Haagerup approximation property for a von Neumann algebra equipped with a faithful normal state is shown to imply existence of unital, -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.
Keywords
Cite
@article{arxiv.1404.6214,
title = {The Haagerup approximation property for von Neumann algebras via quantum Markov semigroups and Dirichlet forms},
author = {Martijn Caspers and Adam Skalski},
journal= {arXiv preprint arXiv:1404.6214},
year = {2015}
}
Comments
26 pages; v3 adds Corollary 5.8, corrects a mistake in Section 3 and updates references; all the main results remain unchanged. The article will appear in the Communications in Mathematical Physics