Structure of mixing and category of complete mixing for stochastic operators
Annales Polonici Mathematici, Tome 56 (1991) no. 3, pp. 233-242
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_ap_56_3_233_242,
author = {A. Iwanik and R. R\k{e}bowski},
title = {Structure of mixing and category of complete mixing for stochastic operators},
journal = {Annales Polonici Mathematici},
pages = {233--242},
year = {1991},
volume = {56},
number = {3},
doi = {10.4064/ap-56-3-233-242},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-56-3-233-242/}
}
TY - JOUR AU - A. Iwanik AU - R. Rębowski TI - Structure of mixing and category of complete mixing for stochastic operators JO - Annales Polonici Mathematici PY - 1991 SP - 233 EP - 242 VL - 56 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/ap-56-3-233-242/ DO - 10.4064/ap-56-3-233-242 LA - en ID - 10_4064_ap_56_3_233_242 ER -
%0 Journal Article %A A. Iwanik %A R. Rębowski %T Structure of mixing and category of complete mixing for stochastic operators %J Annales Polonici Mathematici %D 1991 %P 233-242 %V 56 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/ap-56-3-233-242/ %R 10.4064/ap-56-3-233-242 %G en %F 10_4064_ap_56_3_233_242
A. Iwanik; R. Rębowski. Structure of mixing and category of complete mixing for stochastic operators. Annales Polonici Mathematici, Tome 56 (1991) no. 3, pp. 233-242. doi: 10.4064/ap-56-3-233-242
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