Resumen

CHO, Min-Hyung; RONGLU, Li  y  SWARTZ, Charles. Subseries convergence in abstract duality pairs. Proyecciones (Antofagasta) [online]. 2014, vol.33, n.4, pp.447-470. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172014000400007.

Let E, F be sets, G an Abelian topological group and b : ExF - G. Then (E, F, G) is called an abstract triple. Let w(F, E) be the weakest toplogy on F such that the maps {b(x, ·): x G E} from F into G are continuous. A subset B C F is w(F,E) sequentially conditionally compact if every sequence {yk} C B has a subsequence {y_nk } such that limj; b(x, y_nk) exists for every x G E. It is shown that if a formal series in E is subseries convergent in the sense that for every subsequence {x_nj} there is an element x G E such that Xj=! b(x_nj ,y) = b(x,y) for every y G F ,then the series Xj=! b(x_nj ,y) converge uniformly for y belonging to w(F, E) sequentially conditionally compact subsets ofF. This result is used to establish Orlicz-Pettis Theorems in locall convex and function spaces. Applications are also given to Uniform Boundedness Principles and continuity results for bilinear mappings.

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