A sufficient condition for strong almost-periodicity of scalarly almost periodic representations of the group of real numbers
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We prove the following theorem: If every separable subspace Y of a Banach space X has a separable weak sequential closure in Y **, then every scalarly almost periodic group acting in X is strongly almost periodic.
KeywordsBanach Space Periodic Function Equivalent Norm Separable Banach Space Periodic Group
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- 1.M. I. Kadets and Yu. I. Lyubich, “On relationships between various types of almost periodicity of representations of groups,” Teor. Funk. Funk. Anal. Prilozh., Issue 53, 3–5 (1990).Google Scholar
- 3.Yu. I. Lyubich, Introduction to the Theory of Banach Representations of Groups [in Russian], Vyshcha Shkola, Kharkov (1963).Google Scholar
- 4.Yu. I. Lyubitch, “On conditions of completeness of the system of eigenvectors of a correct operator,” Usp. Mat. Nauk, 18, No. 1, 165–171 (1963).Google Scholar
- 8.C. Bessada and A. Pelczynsky, Selected Topics in Infinite-Dimensional Topology, PWN, Warsaw (1975).Google Scholar