In this paper we study unique ergodicity of C∗-dynamical system (A,T), consisting of a unital C∗-algebra A and a Markov operator T:A↦A, relative to its fixed point subspace, in terms of Riesz summation which is weaker than Cesaro one. Namely, it is proven that (A,T) is uniquely ergodic relative to its fixed point subspace if and only if its Riesz means... converge to ET(x) in A for any x∈A, as n→∞, here ET is an projection of A to the fixed point subspace of T. It is also constructed a uniquely ergodic entangled Markov operator relative to its fixed point subspace, which is not ergodic.

Accardi, L., Farrukh, M. (2009). A Note on noncommutative unique ergodicity and weighted means. LINEAR ALGEBRA AND ITS APPLICATIONS, 430(2-3), 782-790 [10.1016/j.laa.2008.09.029].

A Note on noncommutative unique ergodicity and weighted means

ACCARDI, LUIGI;
2009-01-01

Abstract

In this paper we study unique ergodicity of C∗-dynamical system (A,T), consisting of a unital C∗-algebra A and a Markov operator T:A↦A, relative to its fixed point subspace, in terms of Riesz summation which is weaker than Cesaro one. Namely, it is proven that (A,T) is uniquely ergodic relative to its fixed point subspace if and only if its Riesz means... converge to ET(x) in A for any x∈A, as n→∞, here ET is an projection of A to the fixed point subspace of T. It is also constructed a uniquely ergodic entangled Markov operator relative to its fixed point subspace, which is not ergodic.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/06 - Probabilita' e Statistica Matematica
English
uniquely ergodic; Markov operator; Riesz means
Accardi, L., Farrukh, M. (2009). A Note on noncommutative unique ergodicity and weighted means. LINEAR ALGEBRA AND ITS APPLICATIONS, 430(2-3), 782-790 [10.1016/j.laa.2008.09.029].
Accardi, L; Farrukh, M
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/37107
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