Vector-valued almost convergence and classical properties in normed spaces

被引：0
作者：
A AIZPURU
R ARMARIO*
F J GARCÍA-PACHECO
F J PÉREZ-FERNÁNDEZ
机构：
[1] University of Cadiz,Department of Mathematics
来源：
Proceedings - Mathematical Sciences | 2014年 / 124卷
关键词：
Almost-convergence; almost-summability; completeness; 46B15, 46B20, 40H05;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
页码：93 / 108
页数：15
相关论文
共 32 条
[1]  
Aizpuru A(2011)Banach limits and uniform almost summability J. Math. Anal. Appl. 379 82-90
[2]  
Armario R(2008)Almost summability and unconditionally Cauchy series Bull. Belg. Math. Soc. Simon Stevin 15 635-644
[3]  
García-Pacheco FJ(2007)Matrix summability and uniform convergence of series Proc. Amer. Math. Soc. 135 3571-3579
[4]  
Pérez-Fernández FJ(2003)Boolean algebras and uniform convergence of series J. Math. Anal. Appl. 284 89-96
[5]  
Aizpuru A(2009)Matrix summability methods and weakly unconditionally Cauchy series Rocky Mountain J. Math. 39 367-380
[6]  
Armario R(2000)Spaces of Acta Math. Hungar. 87 135-146
[7]  
Pérez-Fernández FJ(1958)-Bounded multiplier convergent series Stud. Math. 17 151-164
[8]  
Aizpuru A(1999)On bases and unconditional convergence of series in Banach Spaces J. Anal. 7 21-29
[9]  
García-Pacheco FJ(1991)Some remarks on invariant means and almost convergence Analysis 11 279-292
[10]  
Pérez-Eslava C(1997)Consistency theory for operator valued matrices J. Math. Anal. Appl. 207 291-299
1234