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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Algebras of functions on semitopological left-groups
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by John F. Berglund and Paul Milnes PDF
Trans. Amer. Math. Soc. 222 (1976), 157-178 Request permission

Abstract:

We consider various algebras of functions on a semitopological left-group $S = X \times G$, the direct product of a left-zero semigroup X and a group G. In §1 we examine various analogues to the theorem of Eberlein that a weakly almost periodic function on a locally compact abelian group is uniformly continuous. Several appealing conjectures are shown by example to be false. In the second section we look at compactifications of products $S \times T$ of semitopological semigroups with right identity and left identity, respectively. We show that the almost periodic compactification of the product is the product of the almost periodic compactifications, thus generalizing a result of deLeeuw and Glicksberg. The weakly almost periodic compactification of the product is not the product of the weakly almost periodic compactifications except in restrictive circumstances; for instance, when T is a compact group. Finally, as an application, we define and study analytic weakly almost periodic functions and derive the theorem, analogous to a classical theorem about almost periodic functions, that an analytic function which is weakly almost periodic on a single line is analytic weakly almost periodic on a whole strip.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 222 (1976), 157-178
  • MSC: Primary 43A60; Secondary 22A20
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0422998-9
  • MathSciNet review: 0422998