Convergence of iterates of averages of certain operator representations and of convolution powers

Yves Derriennic, Michael Lin

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

1. (1) Let G be a locally compact σ-compact group and let T(t) be a continuous representation of G by isometries in a uniformly convex Banach space B. Let μ be an adapted, strictly aperiodic and spread out probability on G, and let Px = f{hook} T(t)x dμ(t). Then Pn converges strongly. 2. (2) If G is not compact and μ is as above, then ∥μn * f{hook}∥ → 0 for every f{hook} continuous vanishing at infinity.

Original languageEnglish
Pages (from-to)86-102
Number of pages17
JournalJournal of Functional Analysis
Volume85
Issue number1
DOIs
StatePublished - 1 Jan 1989

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