Ergodic sequences and a subspace of B(G)
type: Item
instance of: scholarly article
title: Ergodic sequences and a subspace of B(G)
zbMATH Open document ID: 0671.43002
DOI: 10.1216/RMJ-1988-18-3-681
author: Alan L. T. Paterson
author: Paul Milnes
published in: Rocky Mountain Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The authors generalize a result of Blum and Eisenberg on the convergence of a sequence of probability measures \(\mu_ n\) to non-abelian groups G. The relationship of \(B_ I(G)\) (the closure of the linear span of the coefficients of the irreducible representations of G) to AP(G) (the space of all almost periodic functions) and also to \(C_ 0(G)\) is investigated and \(B_ I(G)\) is identified for some special groups (e.g., the Heisenberg group). Some results (concerning ``ergodic'' sequences \(\mu_ n)\) already follow from \textit{V. Losert} and the reviewer [Invent. Math. 50, 65-74 (1978; Zbl 0414.22006), Theorem 1 solves the problem posed at the end of the paper, see also Theorem 3] and from \textit{K. Gröchenig}, \textit{V. Losert} and the reviewer [Lect. Notes Math. 1210, 97-107 (1985; Zbl 0607.60008)].
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 22D40
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 28D99
Mathematics Subject Classification ID: 43A60
zbMATH DE Number: 4098005
zbMATH Keywords: probability measures
zbMATH Keywords: non-abelian groups
zbMATH Keywords: irreducible representations
zbMATH Keywords: almost periodic functions
zbMATH Keywords: Heisenberg group
MaRDI profile type: Publication
full work available at URL: rmj-1988-18-3-681
OpenAlex ID: W2056254489
description: scientific article; zbMATH DE number 4098005