A note on noncommutative unique ergodicity and weighted means
| dc.creator | Accardi, Luigi | |
| dc.creator | Mukhamedov, Farrukh | |
| dc.date | 2008-03-03 | |
| dc.date | 2008-09-22 | |
| dc.date.accessioned | 2026-07-07T10:03:54Z | |
| dc.date.available | 2026-07-07T10:03:54Z | |
| dc.description | In this paper we study unique ergodicity of $C^*$-dynamical system $(\ga,T)$, consisting of a unital $C^*$-algebra $\ga$ and a Markov operator $T:\ga\mapsto\ga$, relative to its fixed point subspace, in terms of Riesz summation which is weaker than Cesaro one. Namely, it is proven that $(\ga,T)$ is uniquely ergodic relative to its fixed point subspace if and only if its Riesz means {equation*} \frac{1}{p_1+...+p_n}\sum_{k=1}^{n}p_kT^kx {equation*} converge to $E_T(x)$ in $\ga$ for any $x\in\ga$, as $n\to\infty$, here $E_T$ is an projection of $\ga$ 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. | |
| dc.description | 11 pages. submitted. Linear Alg. Applications (to appear) | |
| dc.identifier | https://arxiv.org/abs/0803.0073 | |
| dc.identifier | http://arxiv.org/abs/0803.0073 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169466 | |
| dc.subject | Operator Algebras | |
| dc.subject | Dynamical Systems | |
| dc.subject | 47A35, 46L35, 46L55 | |
| dc.title | A note on noncommutative unique ergodicity and weighted means | |
| dc.type | text |