Communications in Mathematical Analysis

Almost Periodicity in Linear Topological Spaces Revisited

S. M. Alsulami and L. A. Khan

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Almost periodic functions with values in Banach spaces, and even more generally in Fréchet spaces and $p$-Fréchet spaces, have been investigated by many authors. The purpose of this paper is to investigate the extent to which some results of these authors also hold in the setting of topological vector spaces, not necessarily locally convex or $p$-locally convex. In fact, most of our results (Theorems 3.3, 3.5-3.8) do not require even completeness or metrizability of the range space. We thus extend and unify several known results.

Article information

Commun. Math. Anal., Volume 13, Number 1 (2012), 54-63.

First available in Project Euclid: 2 October 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
Secondary: 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 46E40: Spaces of vector- and operator-valued functions

Almost periodic function topological vector space $F$-space uniform topology Bochner Criteria


Khan, L. A.; Alsulami, S. M. Almost Periodicity in Linear Topological Spaces Revisited. Commun. Math. Anal. 13 (2012), no. 1, 54--63.

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