arXiv 0804.18642008-04math.OA

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

B. V. Rajarama Bhat, Franco Fagnola, Michael Skeide

备注：: 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
发表信息：: Infin Dimens Anal Quantum Prob and RelatTop, 11 (2) 2008 523-539
DOI：: 10.1142/S0219025708003269

英文摘要：

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.

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