RT journal article
T1 General methods of convergence and summability
A1 García Pacheco, Francisco Javier
A1 Kama, Ramazan
A1 Listán García, María del Carmen
A2 Matemáticas
K1 Methods
K1 Convergence
K1 Summability
K1 47A05
AB This paper is on general methods of convergence and summability. We first present the general method of convergence described by free filters of N and study the space of convergence associated with the filter. We notice that c(X) is always a space of convergence associated with a filter (the Frechet filter); that if X is finite dimensional, then l infinity (X) is a space of convergence associated with any free ultrafilter of N; and that if X is not complete, then l infinity (X) is never the space of convergence associated with any free filter of N. Afterwards, we define a new general method of convergence inspired by the Banach limit convergence, that is, described through operators of norm 1 which are an extension of the limit operator. We prove that l infinity (X) is always a space of convergence through a certain class of such operators; that if X is reflexive and 1-injective, then c(X) is a space of convergence through a certain class of such operators; and that if X is not complete, then c(X) is never the space of convergence through any class of such operators. In the meantime, we study the geometric structure of the set HB(lim):={T is an element of B(l infinity (X),X):T|c(X)=lim and parallel to T parallel to =1} and prove that HB(lim) is a face of BLX0</mml:msubsup> if X has the Bade property, where LX0</mml:msubsup>:={T is an element of B(<mml:msub>l infinity (X),X):<mml:msub>c0(X)subset of ker(T)}. Finally, we study the multipliers associated with series for the above methods of convergence.
PB SPRINGER
SN 1029-242X
YR 2021
FD 2021-04
LK http://hdl.handle.net/10498/24891
UL http://hdl.handle.net/10498/24891
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026