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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Multipliers for the space of almost-convergent functions on a semigroup
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by Ching Chou and J. Peter Duran PDF
Proc. Amer. Math. Soc. 39 (1973), 125-128 Request permission


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) $|f(x) - \alpha | < \varepsilon$ if $x \in S\backslash A$.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 39 (1973), 125-128
  • MSC: Primary 43A07; Secondary 43A22
  • DOI:
  • MathSciNet review: 0315356