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Keywords:
completeness; barrelledness; weakly unconditionally Cauchy series
completeness; barrelledness; weakly unconditionally Cauchy series
Summary:
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 $.
References:
[aizp] A. Aizpuru and F. J. Pérez-Fernández: Spaces of $\mathcal{S}$-bounded multiplier convergent series. Acta Math. Hungar. 87 (2000), 103–114. DOI 10.1023/A:1006781218759 | MR 1755883
[BP58a] C. Bessaga and A. Pelczynski: On bases and unconditional convergence of series in Banach spaces. Stud. Math. 17 (1958), 151–164. DOI 10.4064/sm-17-2-151-164 | MR 0115069
[Diestel] J. Diestel: Sequences and Series in Banach Spaces. Springer-Verlag, New York, 1984. MR 0737004
[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 10.1090/mmono/086 | MR 1108619
[Mc56] C. W. McArthur: On relationships amongst certain spaces of sequences in an arbitrary Banach space. Canad. J. Math. 8 (1956), 192–197. DOI 10.4153/CJM-1956-022-0 | MR 0078662 | Zbl 0074.32305
[Qingying] Q. Bu and C. Wu: Unconditionally convergent series of operators on Banach spaces. J. Math. Anal. Appl. 207 (1997), 291–299. DOI 10.1006/jmaa.1997.5218 | MR 1438915
[Li] R. Li and Q. Bu: Locally convex spaces containing no copy of $c_0$. J. Math. Anal. Appl. 172 (1993), 205–211. DOI 10.1006/jmaa.1993.1017 | MR 1199505
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