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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/124/01/0093-0108

    • Keywords

       

      Almost-convergence; almost-summability; completeness.

    • Abstract

       

      In this paper we study the almost convergence and the almost summability in normed spaces. Among other things, spaces of sequences defined by the almost convergence and the almost summability are proved to be complete if the basis normed space is so. Finally, some classical properties such as completeness, reflexivity, Schur property, Grothendieck property, and the property of containing a copy of $c_0$ are characterized in terms of the almost convergence.

    • Author Affiliations

       

      A Aizpuru1 R Armario1 F J Garcia-Pacheco1 F J Perez-Fernandez1

      1. Department of Mathematics, University of Cadiz, Puerto Real 11510, Spain

    • Dates

       
      Published
      February 2014
      Manuscript received
      6 August 2012
      Manuscript revised
      7 September 2012

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