Geodesic
Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 889-896 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $.
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 
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     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},
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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/

[aizp] A. Aizpuru and F. J. Pérez-Fernández: Spaces of $\mathcal{S}$-bounded multiplier convergent series. Acta Math. Hungar. 87 (2000), 103–114. | DOI | MR

[BP58a] C. Bessaga and A. Pelczynski: On bases and unconditional convergence of series in Banach spaces. Stud. Math. 17 (1958), 151–164. | DOI | MR

[Diestel] J. Diestel: Sequences and Series in Banach Spaces. Springer-Verlag, New York, 1984. | MR

[Kadets91] V. M. Kadets and M. I. Kadets: Rearrangements of Series in Banach Spaces. Translations of Mathematical Monographs. 86. Amer. Math. Soc., Providence, 1991. | DOI | MR

[Mc56] C. W. McArthur: On relationships amongst certain spaces of sequences in an arbitrary Banach space. Canad. J. Math. 8 (1956), 192–197. | DOI | MR | Zbl

[Qingying] Q. Bu and C. Wu: Unconditionally convergent series of operators on Banach spaces. J. Math. Anal. Appl. 207 (1997), 291–299. | DOI | MR

[Li] R. Li and Q. Bu: Locally convex spaces containing no copy of $c_0$. J. Math. Anal. Appl. 172 (1993), 205–211. | DOI | MR