Geodesic
CHARACTERIZATIONS OF SERIES IN BANACH SPACES
Acta mathematica Universitatis Comenianae, Tome 68 (1999) no. 2 
A. Aizpuru; F. J. Perez-fernandez. CHARACTERIZATIONS OF SERIES IN BANACH SPACES. Acta mathematica Universitatis Comenianae, Tome 68 (1999) no. 2. http://geodesic.mathdoc.fr/item/AMUC_1999_68_2_a12/
@article{AMUC_1999_68_2_a12,
     author = {A. Aizpuru and F. J. Perez-fernandez},
     title = {CHARACTERIZATIONS {OF} {SERIES} {IN} {BANACH} {SPACES}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1999},
     volume = {68},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1999_68_2_a12/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper we prove several new characterizations of weakly unconditionally Cauchy series in Banach spaces and in the dual space of a normed space. For a given series $\zeta$, we consider the spaces $\mathcalS(\zeta)$, $\mathcalS_w(\zeta)$ and $\mathcalS_0(\zeta)$ of bounded sequences of real numbers $(a_i)_i$ such that the series $\sum_i^a_ix_i$ is convergent, weakly convergent or $\ast$-weakly convergent, respectively. By means of these spaces we characterize conditionally and weakly unconditionally Cauchy series.