A random weak ergodic property of infinite products of operators in metric spaces. (2nd January 2019)

• Record Type: Journal Article
• Authors: Reich, Simeon; Zaslavski, Alexander J.
• Is Part Of: Optimization. Volume 68:Number 1(2019)
• Page Start: 51
• Page End: 63
• Publication Date: 2019-01-02
• Subjects: Complete metric space -- hyperbolic space -- infinite product -- random weak ergodic property; 47H07 -- 47H09 -- 47H25 -- 54E35 -- 54E52; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1536754
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We study the random weak ergodic property of infinite products of mappings acting on complete metric spaces. Our results describe an aspect of the asymptotic behaviour of random infinite products of such mappings. More precisely, we show that in appropriate spaces of sequences of operators there exists a subset, which is a countable intersection of open and everywhere dense sets, such that each sequence belonging to this subset has the random weak ergodic property. Then we show that several known results in the literature can be deduced from our general result.