Generalized summing sequences and the mean ergodic theorem
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- by Julius Blum and Bennett Eisenberg PDF
- Proc. Amer. Math. Soc. 42 (1974), 423-429 Request permission
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
- 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), 17–24. MR 374336
- J. R. Blum and V. J. Mizel, On a theorem of Weyl and the ergodic theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 20 (1971), 193–198. MR 306445, DOI 10.1007/BF00534901
- 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 338260, DOI 10.1002/cpa.3160260103
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 423-429
- MSC: Primary 28A65; Secondary 22D40
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330412-0
- MathSciNet review: 0330412