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 on a locally compact abelian group *G* so that, for any strongly continuous unitary representation of *G*, will converge to a *U*-invariant function. These conditions are applied in the case where the group is the integers.

**[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), 17–24. MR**0374336****[2]**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**0306445****[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**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1974-0330412-0

Article copyright:
© Copyright 1974
American Mathematical Society