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Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series

Francisco Javier Pérez Fernández; F. Benítez-Trujillo; Antonio Aizpuru Tomás — 2000

Czechoslovak Mathematical Journal

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 $X^{*}$ .

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