Abstract
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.
Citation
A. Aizpuru. A. Gutiérrez-Dávila. "On the interchange of series and some applications." Bull. Belg. Math. Soc. Simon Stevin 11 (3) 409 - 430, September 2004. https://doi.org/10.36045/bbms/1093351381
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