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arXiv · 0804.1864

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

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

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B. V. Rajarama Bhat, Franco Fagnola, Michael Skeide. 2008-10-19. Maximal Commutative Subalgebras Invariant for CP-Maps: (Counter-)Examples. https://doi.org/10.1142/s0219025708003269

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