ON THE EQUIVALENCE BETWEEN ERGODICITY
AND WEAK MIXING FOR OPERATORS SEMIGROUPS
Mohamed Hmissi1, Farida Mokchaha2
1,2 College of Science
Department of Mathematics and Statistics
Imam Muhammad Ibn Saud Islamic University
Riyadh - 11623, SAUDI ARABIA

Abstract

We prove the equivalence between ergodicity and weak mixing of an invariant probability measure $m$ for strongly continuous contraction semigroups of linear operators on $L^2(m)$ satisfying the sector condition.

The same result is proved for subordinated semigroups in the Bochner sense by the one-sided stable sudordinators.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 2
Year: 2023

DOI: 10.12732/ijam.v36i2.1

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