Uniformly continuous and weakly almost periodic functions on some topological semigroups
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- by Heneri A. M. Dzinotyiweyi PDF
- Proc. Amer. Math. Soc. 114 (1992), 571-574 Request permission
Abstract:
Let $\operatorname {LUC} (S)$ be the space of bounded left uniformly continuous functions and $\operatorname {WAP} (S)$ the space of bounded weakly almost periodic functions on a topological semigroup $S$. For a large class of topological semigroups called stips that are not relatively neocompact, we show that the quotient space $\operatorname {LUC} (S)/\operatorname {WAP} (S)$ contains an isometric linear copy of ${l^\infty }$. The result is particularly interesting on noting that the underlying topological semigroup is not assumed to support an absolutely continuous measure—a theme studied by the author in a previous paper.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 571-574
- MSC: Primary 22A20; Secondary 43A60
- DOI: https://doi.org/10.1090/S0002-9939-1992-1072336-0
- MathSciNet review: 1072336