A note on noncommutative unique ergodicity and weighted means

Accardi, Luigi and Mukhamedov, Farrukh (2009) A note on noncommutative unique ergodicity and weighted means. Linear Algebra and its Applications, 430 (2-3). pp. 782-790. ISSN 0024-3795

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Official URL: http://dx.doi.org/10.1016/j.laa.2008.09.029

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 1 p1 +· · ·+pn �n k=1 pkTkx 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.

Item Type:	Article (Journal)
Additional Information:	5537/13691
Uncontrolled Keywords:	Uniquely ergodic, Markov operator, Riesz means
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	30 Dec 2011 13:49
Last Update:	08 May 2012 21:16
URI:	http://irep.iium.edu.my/id/eprint/13691
Indexed In:	WOS and SCOPUS

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