Abstract
The Haagerup approximation property for a von Neumann algebra equipped with a faithful normal state φ is shown to imply existence of unital, φ-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.
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Communicated by Y. Kawahigashi
MC is supported by the Grant SFB 878 “Groups, geometry and actions”.
AS is partially supported by the Iuventus Plus Grant IP2012 043872.
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Caspers, M., Skalski, A. The Haagerup Approximation Property for von Neumann Algebras via Quantum Markov Semigroups and Dirichlet Forms. Commun. Math. Phys. 336, 1637–1664 (2015). https://doi.org/10.1007/s00220-015-2302-3
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DOI: https://doi.org/10.1007/s00220-015-2302-3