A note on noncommutative unique ergodicity and weighted means

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 relati...

Full description

Bibliographic Details
Main Authors:	Accardi, Luigi, Mukhamedov, Farrukh
Format:	Article
Language:	English English
Published:	Elsevier Science Inc 2009
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/13691/ http://irep.iium.edu.my/13691/ http://irep.iium.edu.my/13691/ http://irep.iium.edu.my/13691/1/almf-laa%282009%29.pdf http://irep.iium.edu.my/13691/4/A_note_on_noncommutative_unique_ergodicity.pdf

id	iium-13691
recordtype	eprints
spelling	iium-136912012-05-08T13:16:00Z http://irep.iium.edu.my/13691/ A note on noncommutative unique ergodicity and weighted means Accardi, Luigi Mukhamedov, Farrukh QA Mathematics 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. Elsevier Science Inc 2009 Article PeerReviewed application/pdf en http://irep.iium.edu.my/13691/1/almf-laa%282009%29.pdf application/pdf en http://irep.iium.edu.my/13691/4/A_note_on_noncommutative_unique_ergodicity.pdf 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 http://dx.doi.org/10.1016/j.laa.2008.09.029 doi:10.1016/j.laa.2008.09.029
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	QA Mathematics
spellingShingle	QA Mathematics Accardi, Luigi Mukhamedov, Farrukh A note on noncommutative unique ergodicity and weighted means
description	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.
format	Article
author	Accardi, Luigi Mukhamedov, Farrukh
author_facet	Accardi, Luigi Mukhamedov, Farrukh
author_sort	Accardi, Luigi
title	A note on noncommutative unique ergodicity and weighted means
title_short	A note on noncommutative unique ergodicity and weighted means
title_full	A note on noncommutative unique ergodicity and weighted means
title_fullStr	A note on noncommutative unique ergodicity and weighted means
title_full_unstemmed	A note on noncommutative unique ergodicity and weighted means
title_sort	note on noncommutative unique ergodicity and weighted means
publisher	Elsevier Science Inc
publishDate	2009
url	http://irep.iium.edu.my/13691/ http://irep.iium.edu.my/13691/ http://irep.iium.edu.my/13691/ http://irep.iium.edu.my/13691/1/almf-laa%282009%29.pdf http://irep.iium.edu.my/13691/4/A_note_on_noncommutative_unique_ergodicity.pdf
first_indexed	2023-09-18T20:22:48Z
last_indexed	2023-09-18T20:22:48Z
_version_	1777408219755315200

A note on noncommutative unique ergodicity and weighted means

Similar Items