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On asymptotic cyclicity of doubly stochastic operators

100%

Bartoszek W.

1999

tom 72

nr 2

145-152

It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports. If moreover P is Frobenius-Perron or Harris then it is strongly asymptotically cyclic.

On concentrated probabilities

100%

Bartoszek W.

1995

tom 61

nr 1

25-38

Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence $g_n ∈ G$ such that $μ^{∗n}(g_n A) ≡ 1$ for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power $μ^{∗k}$ has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological group G.

Strong mixing Markov semigroups on C₁ are meager

63%

Bartoszek W. , Kuna B.

nr 2

311-317

We show that the set of those Markov semigroups on the Schatten class 𝓒₁ such that in the strong operator topology $lim_{t→ ∞}T(t) = Q$, where Q is a one-dimensional projection, form a meager subset of all Markov semigroups.