Structure of mixing and category of complete mixing for stochastic operators

Anzelm Iwanik; Ryszard Rębowski

ArticleOriginal scientific text

Title

Structure of mixing and category of complete mixing for stochastic operators

Authors ¹, ¹

Affiliations

Institute of Mathematics, Technical University of Wrocław Wybrzeże, Wyspiańskiego 27, 50-370 Wrocław, Poland

Abstract

Let T be a stochastic operator on a σ-finite standard measure space with an equivalent σ-finite infinite subinvariant measure λ. Then T possesses a natural "conservative deterministic factor" Φ which is the Frobenius-Perron operator of an invertible measure preserving transformation φ. Moreover, T is mixing ("sweeping") iff φ is a mixing transformation. Some stronger versions of mixing are also discussed. In particular, a notion of *L¹-s.o.t. mixing is introduced and characterized in terms of weak compactness. Finally, it is shown that most stochastic operators are completely mixing and that the same holds for convolution stochastic operators on l.c.a. groups.

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Title

Structure of mixing and category of complete mixing for stochastic operators

Affiliations

Abstract

Bibliography