## 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 {mapping} 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 meansfrac(1, p_{1} + ⋯ + p_{n}) underover(∑, k = 1, n) p_{k} T^{k} xconverge to E_{T} (x) in A for any x ∈ A, as n → ∞, here E_{T} 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.

Original language | English |
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Pages (from-to) | 782-790 |

Number of pages | 9 |

Journal | Linear Algebra and Its Applications |

Volume | 430 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - Jan 15 2009 |

Externally published | Yes |

## Keywords

- Markov operator
- Riesz means
- Uniquely ergodic

## ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics