In this paper we prove the basic matrix theorem of Antosik-Swartz
under weaker hypotheses than the ones they used. We obtain the
converse result for complete normed spaces and generalize
Antosik's interchange theorem for double series in a normed space.
As a consequence, a number of characterizations on convergence in
several spaces of vector sequences are derived. Finally, we obtain
a version of the Orlicz-Pettis theorem for Banach spaces with a
Schauder basis.
Publié le : 2004-09-14
Classification:
basic matrix theorem,
Orlicz-Pettis theorem and space of vector sequences,
46B15,
46BB25,
40A405
@article{1093351381,
author = {Aizpuru, A. and Guti\'errez-D\'avila, A.},
title = {On the interchange of series and some applications},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {11},
number = {1},
year = {2004},
pages = { 409-430},
language = {en},
url = {http://dml.mathdoc.fr/item/1093351381}
}
Aizpuru, A.; Gutiérrez-Dávila, A. On the interchange of series and some applications. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp. 409-430. http://gdmltest.u-ga.fr/item/1093351381/