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Ukrainian Mathematical Journal

, Volume 49, Issue 4, pp 576–580 | Cite as

A sufficient condition for strong almost-periodicity of scalarly almost periodic representations of the group of real numbers

  • M. I. Kadets
Article

Abstract

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.

Keywords

Banach Space Periodic Function Equivalent Norm Separable Banach Space Periodic Group 
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References

  1. 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
  2. 2.
    D. B. Dimitrov and M. I. Kadetz, “On weakly almost periodic functions,” Teor. Funk. Funk. Anal. Prilozh., Issue 16, 150–154 (1972).zbMATHGoogle Scholar
  3. 3.
    Yu. I. Lyubich, Introduction to the Theory of Banach Representations of Groups [in Russian], Vyshcha Shkola, Kharkov (1963).Google Scholar
  4. 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
  5. 5.
    L. Amerio, “Abstract almost-periodic functions and functional equations,” Boll. Unione Math. Ital., 20, No. 8, 267–383 (1963).MathSciNetGoogle Scholar
  6. 6.
    M. I. Kadets and K. D. Kyursten, “The countability of the spectrum of weakly almost periodic functions with values in a Banach space,” Teor. Funk. Funk. Anal. Prilozh., Issue 33, 45–49 (1980).zbMATHGoogle Scholar
  7. 7.
    Yu. I. Petunin and A. N. Plichko, Theory of Characteristics of Subspaces and Its Applications [in Russian], Vyshcha Shkola, Kiev (1980).zbMATHGoogle Scholar
  8. 8.
    C. Bessada and A. Pelczynsky, Selected Topics in Infinite-Dimensional Topology, PWN, Warsaw (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • M. I. Kadets

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