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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Generalized summing sequences and the mean ergodic theorem

Authors: Julius Blum and Bennett Eisenberg
Journal: Proc. Amer. Math. Soc. 42 (1974), 423-429
MSC: Primary 28A65; Secondary 22D40
MathSciNet review: 0330412
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Abstract: Conditions are found on a sequence of probability measures $ {\mu _n}$ on a locally compact abelian group G so that, for any strongly continuous unitary representation of G, $ \smallint {U_g}f\;d{\mu _n}$ will converge to a U-invariant function. These conditions are applied in the case where the group is the integers.

References [Enhancements On Off] (What's this?)

  • [1] J. R. Blum, B. Eisenberg and L. S. Hahn, Ergodic theory and the measure of sets in the Bohr group, Acta Sci. Math. (Szeged). 34 (1973), 17-34. MR 0374336 (51:10536)
  • [2] J. R. Blum and V. Mizel, On a theorem of Weyl and the ergodic theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 20 (1971), 193-198. MR 0306445 (46:5571)
  • [3] Frederick P. Greenleaf, Ergodic theorems and the construction of summing sequences in amenable locally compact groups, Comm. Pure Appl. Math. 26 (1973), 29-46. MR 0338260 (49:3026)

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