Quantum Markov Semigroups (Product Systems and Subordination)
Operator Algebras
2007-05-23 v2
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.
Cite
@article{arxiv.math/0510653,
title = {Quantum Markov Semigroups (Product Systems and Subordination)},
author = {Paul S. Muhly and Baruch Solel},
journal= {arXiv preprint arXiv:math/0510653},
year = {2007}
}
Comments
Revised according to the referee's comments and suggestions; to appear in International Journal of Mathematics