%0 Journal Article
%T The Haagerup approximation property for von Neumann algebras via quantum Markov semigroups and Dirichlet forms
%A Martijn Caspers
%A Adam Skalski
%J Mathematics
%D 2014
%I arXiv
%R 10.1007/s00220-015-2302-3
%X 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.
%U http://arxiv.org/abs/1404.6214v3