Maximal Commutative Subalgebras Invariant for CP-Maps: (Counter-)Examples
Operator Algebras
2013-11-20 v3
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.
Cite
@article{arxiv.0804.1864,
title = {Maximal Commutative Subalgebras Invariant for CP-Maps: (Counter-)Examples},
author = {B. V. Rajarama Bhat and Franco Fagnola and Michael Skeide},
journal= {arXiv preprint arXiv:0804.1864},
year = {2013}
}
Comments
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