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...
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| Format: | Article |
| Language: | English English |
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Elsevier Science Inc
2009
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| Online Access: | 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 |
| _version_ | 1825645422621753344 |
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| author | Accardi, Luigi Mukhamedov, Farrukh |
| author_facet | Accardi, Luigi Mukhamedov, Farrukh |
| author_sort | Accardi, Luigi |
| collection | IIUM |
| 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. |
| first_indexed | 2024-03-05T22:47:30Z |
| format | Article |
| id | oai:generic.eprints.org:13691 |
| institution | International Islamic University Malaysia |
| language | English English |
| last_indexed | 2024-03-05T22:47:30Z |
| publishDate | 2009 |
| publisher | Elsevier Science Inc |
| record_format | dspace |
| spelling | oai:generic.eprints.org: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 |
| spellingShingle | QA Mathematics Accardi, Luigi Mukhamedov, Farrukh A note on noncommutative unique ergodicity and weighted means |
| title | 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_short | A note on noncommutative unique ergodicity and weighted means |
| title_sort | note on noncommutative unique ergodicity and weighted means |
| topic | QA Mathematics |
| url | 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 |
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