Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series

Authors: Pérez-Fernández F.J.¹; Benitez-Trujillo F.²; Aizpuru A.³

Source: Czechoslovak Mathematical Journal, Volume 50, Number 4, December 2000 , pp. 889-896(8)

Publisher: Springer

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Abstract:

In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space X can be characterized through the behaviour of its weakly-* unconditionally Cauchy series in X*.

Keywords: completeness; barrelledness; weakly unconditionally Cauchy series

Language: English

Document Type: Research article

Affiliations: 1: Departamento de Matemáticas. Universidad de Cádiz, P.O.Box 40, 11510-Puerto Real, Cádiz, Spain, Javier.perez@uca.es 2: Departamento de Matemáticas. Universidad de Cádiz, P.O.Box 40, 11510-Puerto Real, Cádiz, Spain, quico.benitez@uca.es 3: Departamento de Matemáticas. Universidad de Cádiz, P.O.Box 40, 11510-Puerto Real, Cádiz, Spain, antonio.aizpuru@uca.es

Publication date: 2000-12-01