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Mat. Zametki, 1996, Volume 60, Issue 3, Pages 370–382 (Mi mz1837)  

This article is cited in 1 scientific paper (total in 1 paper)

Weight functions on groups and an amenability criterion for Beurling algebras

R. I. Grigorchuk

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The paper is devoted to the study of weights on groups. A connection between weight functions and harmonic functions is established. A relationship between the weight theory on groups with the “Tychonoff property” and the theory of bounded cohomology is presented. It is proved that the Beurling algebra $l^1(G,\omega)$ constructed for the weight $\omega$ is amenable if and only if the group $G$ is amenable and the weight $\omega$ is equivalent to a multiplicative character $\chi\colon G\to\mathbb R_+$.

DOI: https://doi.org/10.4213/mzm1837

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English version:
Mathematical Notes, 1996, 60:3, 274–282

Bibliographic databases:

UDC: 512
Received: 27.12.1995

Citation: R. I. Grigorchuk, “Weight functions on groups and an amenability criterion for Beurling algebras”, Mat. Zametki, 60:3 (1996), 370–382; Math. Notes, 60:3 (1996), 274–282

Citation in format AMSBIB
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\paper Weight functions on groups and an amenability criterion for Beurling algebras
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\transl
\jour Math. Notes
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\pages 274--282
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Shtern, AI, “Triviality and continuity of pseudocharacters and pseudorepresentations”, Russian Journal of Mathematical Physics, 5:1 (1997), 135  mathscinet  zmath  isi
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