Quantum Markov Semigroups (Product Systems and Subordination)

Details Quantum Markov Semigroups (Product Systems and Subordination) Quantum Markov Semigroups (Product Systems and Subordination)

2005-10-30

arxiv.org/abs/math/0510653v2

Mathematics

Operator Algebras

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

Scientific paper

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.

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