Ergodic sequences of probability measures on commutative hypergroups
type: Item
instance of: scholarly article
title: Ergodic sequences of probability measures on commutative hypergroups
zbMATH Open document ID: 1064.43009
DOI: 10.1155/S0161171204305041
author: Liliana Pavel
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51365
review text: An analogue of a result of \textit{J. Blum} and \textit{B. Eisenberg} [Proc. Am. Math. Soc. 42, 423--429 (1974; Zbl 0252.43002)] concerning strongly ergodic sequences (generalized summing sequences) on locally compact abelian groups is proved in this paper in the setting of commutative hypergroups. In the Blum-Eisenberg's result an equivalent condition for the strong ergodicity of a sequence is the weak convergence to the Haar measure on the Bohr compactification of the group. Since the Bohr compactification of a hypergroup does not necessarily carry an extending hypergroup structure, that condition is replaced in this paper by the weak*-convergence to the unique invariant mean on the closure of the linear span of the set of coefficient functions of the representations of the commutative hypergroup.
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 43A62
Mathematics Subject Classification ID: 43A30
zbMATH DE Number: 2168616
zbMATH Keywords: ergodic sequence
zbMATH Keywords: commutative hypergroup
zbMATH Keywords: invariant mean
reviewed by: Mădălina Buneci
MaRDI profile type: Publication
OpenAlex ID: W2034697303
description: scientific article; zbMATH DE number 2168616