ON THE ENTANGLED ERGODIC THEOREM

Author:

FIDALEO FRANCESCO1

Affiliation:

1. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma 00133, Italy

Abstract

Let U be a unitary operator acting on the Hilbert space [Formula: see text], and α: {1, …, m} ↦ {1, …, k} a partition of the set {1, …, m}. We show that the ergodic average [Formula: see text] converges in the weak operator topology if the Aj belong to the algebra of all the compact operators on [Formula: see text]. We write esplicitly the formula for these ergodic averages in the case of pair-partitions. Some results without any restriction on the operators Aj are also presented in the almost periodic case.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

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1. On the Uniform Convergence of Ergodic Averages for $$C^*$$-Dynamical Systems;Mediterranean Journal of Mathematics;2020-07-02

2. Ergodic properties of the Anzai skew-product for the non-commutative torus;Ergodic Theory and Dynamical Systems;2020-01-14

3. Uniform Convergence of Cesaro Averages for Uniquely Ergodic C*-Dynamical Systems;Entropy;2018-12-19

4. Pointwise entangled ergodic theorems for Dunford–Schwartz operators;Banach Journal of Mathematical Analysis;2018-07

5. On the pointwise entangled ergodic theorem;Journal of Mathematical Analysis and Applications;2017-05

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