Maximal Commutative Subalgebras Invariant for CP-Maps: (Counter-)Examples

Abstract

We solve, mainly by counterexamples, many natural questions regarding maximal commutative subalgebras invariant under CP-maps or semigroups of CP-maps on a von Neumann algebra. In particular, we discuss the structure of the generators of norm continuous semigroups on B(G) leaving a maximal commutative subalgebra invariant and show that there exists Markov CP-semigroups on M_d without invariant maximal commutative subalgebras for any d>2.

After the elemenitation in Version 2 of a false class of examples in Version 1, we now provide also correct examples for unital CP-maps and Markov semigroups on M_d for d>2 without invariant masas

References in corpus (1)

• Generators of Detailed Balance Quantum Markov Semigroups

Cited by in corpus (2)

• Structure of Uniformly Continuous Quantum Markov Semigroups
• On the generators of quantum dynamical semigroups with invariant subalgebras