Publication: Ideal Convergence and Completeness of a Normed Space
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Date
2019-10-01
Authors
Leon-Saavedra, Fernando
Javier Perez-Fernandez, Francisco
Romero de la Rosa, Maria del Pilar
Sala, Antonio
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Mdpi
Abstract
We aim to unify several results which characterize when a series is weakly unconditionally Cauchy (wuc) in terms of the completeness of a convergence space associated to the wuc series. If, additionally, the space is completed for each wuc series, then the underlying space is complete. In the process the existing proofs are simplified and some unanswered questions are solved. This research line was originated in the PhD thesis of the second author. Since then, it has been possible to characterize the completeness of a normed spaces through different convergence subspaces (which are be defined using different kinds of convergence) associated to an unconditionally Cauchy sequence.
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Keywords
ideal convergence, unconditionally Cauchy series, completeness, barrelledness, Matrix summability, Series