Vector-Valued almost Convergence and Classical Properties in Normed Spaces

Proceedings Mathematical Sciences

F J Perez-Fernandez¹  A Aizpuru²  R Armario¹  F J Garcia-Pacheco¹ 

[1] $$;Department of Mathematics, University of Cadiz, Puerto Real 0, Spain$$

关键词: Almost-convergence;    almost-summability;    completeness.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 𝑐0 are characterized in terms of the almost convergence.

【 授权许可】

Unknown