Ergodic properties of Markov semigroups in von Neumann algebras

Autores: Katarzyna Kielanowicz, Andrzej Luczak
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 64, Nº 1, 2020, págs. 283-331
Idioma: inglés
DOI: 10.5565/publmat6412012
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Resumen
- We investigate ergodic properties of Markov semigroups in von Neumann algebras with the help of the notion of constrictor, which expresses the idea of closeness of the orbits of the semigroup to some set, as well as the notion of "generalised averages", which generalises to arbitrary abelian semigroups the classical notions of Ces`aro, Borel, or Abel means. In particular, mean ergodicity, asymptotic stability, and structure properties of the ﬁxed-point space are analysed in some detail.