Characterizations of amenable groups
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- by William R. Emerson PDF
- Trans. Amer. Math. Soc. 241 (1978), 183-194 Request permission
Abstract:
Generalizing a construction of Banach from 1923 we obtain new criteria for the amenability of a locally compact group G. The relationship of these new criteria to known characterizations is then investigated, and in particular a formally strenghthened version of the von Neumann/Dixmier condition for amenability is established.References
- Richard Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839–848. MR 45941, DOI 10.1090/S0002-9939-1951-0045941-1 S. Banach, Sur le problème de la mesure, Fund. Math. 4 (1923), 7-31.
- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549 E. Hewitt and K. A. Ross, Abstract harmonic analysis. I, Academic Press, New York, 1963.
- James C. S. Wong, Topologically stationary locally compact groups and amenability, Trans. Amer. Math. Soc. 144 (1969), 351–363. MR 249536, DOI 10.1090/S0002-9947-1969-0249536-4
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 241 (1978), 183-194
- MSC: Primary 43A07; Secondary 43A15
- DOI: https://doi.org/10.1090/S0002-9947-1978-0492296-8
- MathSciNet review: 492296