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

Lau, Anthony; Losert, Viktor

doi:10.1090/S0002-9947-99-02242-4

Ergodic sequences in the Fourier-Stieltjes algebra and measure algebra of a locally compact group
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by Anthony To-Ming Lau and Viktor Losert

Trans. Amer. Math. Soc. 351 (1999), 417-428

DOI: https://doi.org/10.1090/S0002-9947-99-02242-4

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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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