Ergodic properties of Markov semigroups in von Neumann algebras

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 abeli...

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Detalles Bibliográficos
Autores: Kielanowicz, Katarzyna, Łuczak, Andrzej
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:218573
Acceso en línea:https://ddd.uab.cat/record/218573
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6412012
Access Level:acceso abierto
Palabra clave:Ergodic theorems
Markov semigroups
Positive maps
Von Neumann algebra
Descripción
Sumario: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.