Quantum Markov Semigroups (Product Systems and Subordination)

Abstract

We show that if a product system comes from a quantum Markov semigroup, then it carries a natural Borel structure with respect to which the semigroup may be realized in terms of a measurable representation. We show, too, that the dual product system of a Borel product system also carries a natural Borel structure. We apply our analysis to study the order interval consisting of all quantum Markov semigroups that are subordinate to a given one.

Revised according to the referee's comments and suggestions; to appear in International Journal of Mathematics

References in corpus (1)

• Von Neumann Modules, Intertwiners and Self-Duality

Cited by in corpus (2)

• Product Systems; a Survey with Commutants in View
• Representations of product systems over semigroups and dilations of commuting CP maps