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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniformly continuous and weakly almost periodic functions on some topological semigroups


Author: Heneri A. M. Dzinotyiweyi
Journal: Proc. Amer. Math. Soc. 114 (1992), 571-574
MSC: Primary 22A20; Secondary 43A60
MathSciNet review: 1072336
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1072336-0
PII: S 0002-9939(1992)1072336-0
Keywords: Topological semigroup, uniformly continuous functions, weakly almost periodic functions
Article copyright: © Copyright 1992 American Mathematical Society