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Unconditionally Cauchy series and Cesàro summability |
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| Authors: | A Aizpuru A Gutiérrez-Dávila |
| Institution: | Departamento de Matemáticas, Universidad de Cádiz, Apdo. 40, 11510-Puerto Real (Cádiz), Spain |
| Abstract: | In this paper we obtain new characterizations of weakly unconditionally Cauchy series and unconditionally convergent series through Cesàro summability. We study new spaces associated to a series in a Banach space; as a consequence, new characterizations of complete and barrelled normed spaces are proved. |
| Keywords: | (Weakly) unconditionally Cauchy series Cesà ro-convergence Weak (and weak-*) Cesà ro-convergence Orlicz-Pettis theorem Completeness and barrelledness |
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