Geodesic
Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 889-896

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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-$\ast $ unconditionally Cauchy series in $X^\ast $.
Classification : 40A05, 46B15, 46B45
Keywords: completeness; barrelledness; weakly unconditionally Cauchy series 
@article{CMJ_2000__50_4_a15,
     author = {P\'erez-Fern\'andez, F. J. and Ben{\'\i}tez-Trujillo, F. and Aizpuru, A.},
     title = {Characterizations of completeness of normed spaces through weakly unconditionally {Cauchy} series},
     journal = {Czechoslovak Mathematical Journal},
     pages = {889--896},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2000},
     mrnumber = {1792978},
     zbl = {1079.46505},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000__50_4_a15/}
}
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Pérez-Fernández, F. J.; Benítez-Trujillo, F.; Aizpuru, A. Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 889-896. http://geodesic.mathdoc.fr/item/CMJ_2000__50_4_a15/