scholarly journals Almost summability and unconditionally Cauchy series

2008 ◽  
Vol 15 (4) ◽  
pp. 635-644 ◽  
Author(s):  
A. Aizpuru ◽  
R. Armario ◽  
F.J. Pérez-Fernández
Keyword(s):  
Cauchy Series

scholarly journals Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series

2000 ◽  
Vol 50 (4) ◽  
pp. 889-896 ◽  
Author(s):  
F. J. Pérez-Fernández ◽  
F. Benitez-Trujillo ◽  
A. Aizpuru
Keyword(s):  
Normed Spaces ◽  
Weakly Unconditionally Cauchy Series ◽  
Cauchy Series

UNCONDITIONAL CAUCHY SERIES AND UNIFORM CONVERGENCE ON MATRICES

2004 ◽  
Vol 25 (03) ◽  
pp. 335-346 ◽  
Author(s):  
A. AIZPURU ◽  
A. GUTIÉRREZ-DÁVILA
Keyword(s):  
Uniform Convergence ◽  
Cauchy Series

Weak unconditional Cauchy series

1980 ◽  
Vol 29 (3) ◽  
pp. 364-368 ◽  
Author(s):  
P. K. Kamthan ◽  
Manjul Gupta
Keyword(s):  
Cauchy Series

scholarly journals Unconditionally converging polynomials on Banach spaces

1995 ◽  
Vol 117 (2) ◽  
pp. 321-331 ◽  
Author(s):  
Manuel Gonz´lez ◽  
Joaquín M. Gutiérrez
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Weak Topology ◽  
Linear Operators ◽  
Null Sequence ◽  
Good Tool ◽  
Image Position ◽  
Weakly Unconditionally Cauchy Series ◽  
Cauchy Series

In the study of polynomials acting on Banach spaces, the weak topology is not such a good tool as in the case of linear operators, due to the bad behaviour of the polynomials with respect to the weak convergence. For example,is a continuous polynomial taking a weakly null sequence into a sequence having no weakly Cauchy subsequences. In this paper we show that the situation is not so bad for unconditional series. Recall that is a weakly unconditionally Cauchy series (in short a w.u.C. series) in a Banach space E if for every f ε E* we have that and is an unconditionally converging series (in short an u.c. series) if every subseries is norm convergent.

scholarly journals Unconditionally Cauchy series and Cesàro summability

2006 ◽  
Vol 324 (1) ◽  
pp. 39-48 ◽  
Author(s):  
A. Aizpuru ◽  
A. Gutiérrez-Dávila ◽  
A. Sala
Keyword(s):  
Cesàro Summability ◽  
Cesaro Summability ◽  
Cauchy Series

scholarly journals Completeness of a normed space via strong p-Cesàro summability

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3013-3022 ◽  
Author(s):  
F. Léon-Saavedra ◽  
S. Moreno-Pulido ◽  
A. Sala-Pérez
Keyword(s):  
Normed Space ◽  
Convergent Series ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Weakly Unconditionally Cauchy Series ◽  
Unconditionally Convergent Series ◽  
Cauchy Series

In this paper we will characterize the completeness and barrelledness of a normed space through the strong p-Ces?ro summability of series. A new characterization of weakly unconditionally Cauchy series and unconditionally convergent series through the strong p-Ces?ro summability is obtained.

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