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Almost-convergence; almost-summability; completeness.

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.

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

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

Published

February 2014

Manuscript received

6 August 2012

Manuscript revised

7 September 2012