Weakly almost periodic elements in of a locally compact group

Authors:
Anthony To Ming Lau and James C. S. Wong

Journal:
Proc. Amer. Math. Soc. **107** (1989), 1031-1036

MSC:
Primary 43A15; Secondary 22D25, 43A07

DOI:
https://doi.org/10.1090/S0002-9939-1989-0991701-0

MathSciNet review:
991701

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Abstract: Let be a locally compact abelian group with dual group acting on by pointwise multiplication. We show that if contains a nonzero element such that is relatively compact in the weak (or norm) topology of , then is discrete. In this case is relatively compact in the weak or norm topology of if and only if vanishes at infinity. A related result when acts on the von Neumann algebra is also determined.

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0991701-0

Article copyright:
© Copyright 1989
American Mathematical Society