MATRIX SUMMABILITY METHODS AND WEAKLY UNCONDITIONALLY CAUCHY SERIES

We study new sequence spaces determined by series in normed spaces and a matrix summability method, giving new characterizations of weakly unconditionally Cauchy series. We obtain characterizations for the completeness of a normed space, and a version of the Orlicz-Pettis theorem via matrix summabil...

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2009-01, Vol.39 (2), p.367-380
Main Authors: AIZPURU, A., PÉREZ-ESLAVA, C., SEOANE-SEPÚLVEDA, J.B.
Format: Article
Language:English
Subjects:
40C05
46B15
46B45
Banach space
Mathematical completeness
Mathematical sequences
Mathematical theorems
Matrices
Matrix summability
Orlicz-Pettis theorem
Series convergence
Sufficient conditions
weakly unconditionally Cauchy series
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Summary:We study new sequence spaces determined by series in normed spaces and a matrix summability method, giving new characterizations of weakly unconditionally Cauchy series. We obtain characterizations for the completeness of a normed space, and a version of the Orlicz-Pettis theorem via matrix summability methods is also proved.
ISSN:0035-7596
1945-3795
DOI:10.1216/RMJ-2009-39-2-367