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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Characterizations of amenable groups

Author: William R. Emerson
Journal: Trans. Amer. Math. Soc. 241 (1978), 183-194
MSC: Primary 43A07; Secondary 43A15
MathSciNet review: 492296
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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 [Enhancements On Off] (What's this?)

  • [1] R. Arens, The adjoint of a bilinear operator, Proc. Amer. Math. Soc. 2 (1951), 839-848. MR 0045941 (13:659f)
  • [2] S. Banach, Sur le problème de la mesure, Fund. Math. 4 (1923), 7-31.
  • [3] F. P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Math. Studies, No. 16, Van Nostrand, New York, 1969. MR 0251549 (40:4776)
  • [4] E. Hewitt and K. A. Ross, Abstract harmonic analysis. I, Academic Press, New York, 1963.
  • [5] J. C. S. Wong, Topologically stationary locally compact groups and amenability, Trans. Amer. Math. Soc. 144 (1969), 351-363. MR 0249536 (40:2781)

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Keywords: Amenable group, invariant mean
Article copyright: © Copyright 1978 American Mathematical Society

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