RT journal article
T1 Ideal Convergence and Completeness of a Normed Space
A1 León Saavedra, Fernando
A1 Pérez Fernández, Francisco Javier
A1 Romero de la Rosa, María Pilar
A1 Sala Pérez, Antonio
A2 Matemáticas
K1 ideal convergence
K1 unconditionally Cauchy series
K1 completeness
K1 barrelledness
AB We aim to unify several results which characterize when a series is weakly unconditionallyCauchy (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. Thisresearch line was originated in the PhD thesis of the second author. Since then, it has been possible tocharacterize the completeness of a normed spaces through different convergence subspaces (which arebe defined using different kinds of convergence) associated to an unconditionally Cauchy sequence.
PB MDPI
SN 2227-7390
YR 2019
FD 2019-10
LK http://hdl.handle.net/10498/22137
UL http://hdl.handle.net/10498/22137
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 22-sep-2026