Aizpuru, A.Pérez Eslava, C.Seoane Sepúlveda, Juan Benigno2023-06-202023-06-2020060024-379510.1016/j.laa.2006.02.041https://hdl.handle.net/20.500.14352/50494We show that there exist infinite dimensional spaces of series, every non-zero element of which, enjoys certain pathological property. Some of these properties consist on being (i) conditional convergent, (ii) divergent, or (iii) being a subspace of l(infinity) of divergent series. We also show that the space 1(1)(omega)(X) of all weakly unconditionally Cauchy series in X has an infinite dimensional vector space of non-weakly convergent series, and that the set of unconditionally convergent series on X contains a vector space E, of infinite dimension, so that if x is an element of E \ {0} then Sigma(i) parallel to x(i)parallel to = infinity.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0024379506001315http://www.sciencedirect.comrestricted access517.98LineabilityConditionally convergent seriesDivergent seriesVector seriesAnálisis funcional y teoría de operadores