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Ergodic sequences in the Fourier-Stieltjes algebra and measure algebra of a locally compact group

Author(s): Anthony To-Ming Lau; Viktor Losert
Journal: Trans. Amer. Math. Soc. 351 (1999), 417-428.
MSC (1991): Primary 43A05, 43A35
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Abstract: Let $G$ be a locally compact group. Blum and Eisenberg proved that if $G$ is abelian, then a sequence of probability measures on $G$ is strongly ergodic if and only if the sequence converges weakly to the Haar measure on the Bohr compactification of $G.$ In this paper, we shall prove an extension of Blum and Eisenberg's Theorem for ergodic sequences in the Fourier-Stieltjes algebra of $G.$ We shall also give an improvement to Milnes and Paterson's more recent generalization of Blum and Eisenberg's result to general locally compact groups, and we answer a question of theirs on the existence of strongly (or weakly) ergodic sequences of measures on $G.$

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Additional Information:

Anthony To-Ming Lau
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: tlau@vega.math.ualberta.ca

Viktor Losert
Affiliation: Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
Email: losert@pap.univie.ac.at

DOI: 10.1090/S0002-9947-99-02242-4
PII: S 0002-9947(99)02242-4
Keywords: Ergodic sequences, Fourier-Stieltjes algebra, measure algebra, amenable groups
Received by editor(s): February 3, 1997
Additional Notes: This research is supported by NSERC Grant A7679
Copyright of article: Copyright 1999, American Mathematical Society

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