• Weak convergence and weak compactness in the space of almost periodic functions on the real line

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    • Keywords

       

      Almost periodic functions; weak convergence and weak compactness in spaces of continuous functions

    • Abstract

       

      We give necessary and sufficient conditions for sequences in the space AP(R) of continuous almost periodic functions on the real line to converge in the weak topology. The abstract results are illustrated by a number of examples which show that weak convergence seems to be a rare phenomenon. We also characterize the weakly compact subsets in AP(R). In particular, earlier statements made in the monograph by Dunford and Schwartz are refined and completed. We close with some open problems.

    • Author Affiliations

       

      J Batt1 M V Deshpande2

      1. Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresienstraße 39, München - 80333, Germany
      2. Department of Mathematics, Indian Institute of Technology, Powai, Bombay - 400076, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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