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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English English |
| Published: |
Elsevier Science Inc
2009
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| Subjects: | |
| 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 |
| Summary: | 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. |
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