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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Almost convergent and weakly almost periodic functions on a semigroup


Author: Heneri A. M. Dzinotyiweyi
Journal: Trans. Amer. Math. Soc. 277 (1983), 125-132
MSC: Primary 43A60; Secondary 22A20
MathSciNet review: 690044
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Abstract: Let $ S$ be a topological semigroup, $ {\text{US}}(S)$ the set of all bounded uniformly continuous functions on $ S,{\text{WAP(}}S)$ the set of all (bounded) weakly almost periodic functions on $ S,{E_0}(S): = \{ f \in {\text{UC(}}S):m(\vert f\vert) = 0$ for each left and right invariant mean $ m$ on $ {\text{UC(}}S)\} $ and $ {W_0}(S): = \{ f \in {\text{WAP}}(S):\:m(\vert f\vert) = 0$ for each left and right invariant mean $ m$ on $ {\text{WAP(}}S)\} $.

Among other results, for a large class of noncompact locally compact topological semigroups $ S$, we show that the quotient space $ {E_0}(S)/{W_0}(S)$ contains a linear isometric copy of $ {l^\infty }$ and so is nonseparable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0690044-1
PII: S 0002-9947(1983)0690044-1
Keywords: Topological semigroup, almost convergent functions, weakly almost periodic functions, invariant mean
Article copyright: © Copyright 1983 American Mathematical Society