RT Journal Article
T1 Ideal Convergence and Completeness of a Normed Space
A1 Leon-Saavedra, Fernando
A1 Javier Perez-Fernandez, Francisco
A1 Romero de la Rosa, Maria del Pilar
A1 Sala, Antonio
K1 ideal convergence
K1 unconditionally Cauchy series
K1 completeness
K1 barrelledness
K1 Matrix summability
K1 Series
AB 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.
PB Mdpi
YR 2019
FD 2019-10-01
LK http://hdl.handle.net/10668/19291
UL http://hdl.handle.net/10668/19291
LA en
DS RISalud
RD Apr 11, 2025