Publication: Matrix summability methods and weakly unconditionally Cauchy series.
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Publication Date
2009
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Rocky MT Math Consortim
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Abstract
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.
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A. Aizpuru, A. Gutiérrez and A. Sala, Unconditionally Cauchy series and Cesàro summability, preprint.
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F.J. Pérez, F. Benitez and A. Aizpuru, Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series, Czechoslovak Math. J. 50 (2000), 889-896.