von Neumann代数中Markov半群的遍历性质

Pub Date : 2020-01-01 DOI:10.5565/publmat6412012

K. Kielanowicz, A. Luczak

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引用次数: 0

摘要

我们研究了冯诺依曼代数中马尔可夫半群的遍历性质，借助了缩表的概念，它表达了半群轨道与某个集合的接近性，以及“广义平均”的概念，它将经典的Ces’aro、Borel或Abel means的概念推广到任意阿贝尔半群。特别详细地分析了不动点空间的平均遍历性、渐近稳定性和结构性质。

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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 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.

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