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arXiv · 1106.0287

Decomposition of operator semigroups on W*-algebras

András Bátkai·Ulrich Groh·Dávid Kunszenti-Kovács·Marco Schreiber
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Abstract

We consider semigroups of operators on a W$^*$-algebra and prove, under appropriate assumptions, the existence of a Jacobs-DeLeeuw-Glicksberg type decomposition. This decomposition splits the algebra into a "stable" and "reversible" part with respect to the semigroup and yields, among others, a structural approach to the Perron-Frobenius spectral theory for completely positive operators on W$^*$-algebras.

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András Bátkai, Ulrich Groh, Dávid Kunszenti-Kovács, Marco Schreiber. 2011-11-14. Decomposition of operator semigroups on W*-algebras. https://doi.org/10.1007/s00233-011-9362-2

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