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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Multipliers for the space of almost-convergent functions on a semigroup


Authors: Ching Chou and J. Peter Duran
Journal: Proc. Amer. Math. Soc. 39 (1973), 125-128
MSC: Primary 43A07; Secondary 43A22
DOI: https://doi.org/10.1090/S0002-9939-1973-0315356-1
MathSciNet review: 0315356
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Abstract: Let $ S$ be a countably infinite left amenable cancellative semigroup, $ FL(S)$ the space of left almost-convergent functions on $ S$. The purpose of this paper is to show that the following two statements concerning a bounded real function $ f$ on $ S$ are equivalent: (i) $ f \cdot FL(S) \subset FL(S)$; (ii) there is a constant $ \alpha $ such that for each $ \varepsilon > 0$ there exists a set $ A \subset S$ satisfying (a) $ \varphi ({X_A}) = 0$ for each left invariant mean $ \varphi $ on $ S$ and (b) $ \vert f(x) - \alpha \vert < \varepsilon $ if $ x \in S\backslash A$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0315356-1
Keywords: Amenable semigroups, almost-convergence, multipliers, invariant means, weak Cauchy sequences
Article copyright: © Copyright 1973 American Mathematical Society