von Neumann代数中Markov半群的遍历性质

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques 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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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.