KMS Dirichlet forms, coercivity and superbounded Markovian semigroups

Abstract: We provide a new construction of Dirichlet forms on von Neumann algebras associated to eigenvalues of the modular operator of f.n. non tracial states. We describe their structure in terms of derivations and prove coercivity bounds, from which the spectral growth rate are derived. We also introduce a regularizing property of Markovian semigroups (superboundedness) stronger than hypercontractivity, in terms of noncommutative Lp(M)spaces. We also prove superboundedness for the Markovian semigroups associated to the class of Dirichlet forms introduced above, for type I factors M. We then apply this tools to provide a general construction of the quantum Ornstein-Uhlembeck semigroups of the CCR and some of their non-perturbative deformations.

operator algebras

Audience: researchers in the topic

Conference on operator algebras and related topics in Istanbul, 2021