General methods of convergence and summability

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dc.authoridGarcia-Pacheco, Francisco/0000-0001-6208-6071
dc.contributor.authorJavier Garcia-Pacheco, Francisco
dc.contributor.authorKama, Ramazan
dc.contributor.authordel Carmen Listan-Garcia, Maria
dc.date.accessioned2024-12-24T19:29:54Z
dc.date.available2024-12-24T19:29:54Z
dc.date.issued2021
dc.departmentSiirt Üniversitesi
dc.description.abstractThis 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 B-LX(0) if X has the Bade property, where L-X(0):={T is an element of B(l(infinity)(X),X):c(0)(X)subset of ker(T)}. Finally, we study the multipliers associated with series for the above methods of convergence.
dc.description.sponsorshipMinisterio de Ciencia, Innovacion y Universidades [PGC2018-101514-B-100]; Junta de Andalucia [FQM-257]; Plan Propio de la Universidad de Cadiz; 2014-2020 ERDF Operational Programme; Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia [FEDER-UCA18-108415]
dc.description.sponsorshipThe first and third authors are supported by Ministerio de Ciencia, Innovacion y Universidades under PGC2018-101514-B-100, by Junta de Andalucia FQM-257, and Plan Propio de la Universidad de Cadiz. This work has been co-financed by the 2014-2020 ERDF Operational Programme and by the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia. Project reference: FEDER-UCA18-108415.
dc.identifier.doi10.1186/s13660-021-02587-x
dc.identifier.issn1029-242X
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85103587314
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1186/s13660-021-02587-x
dc.identifier.urihttps://hdl.handle.net/20.500.12604/7301
dc.identifier.volume2021
dc.identifier.wosWOS:000636464600001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofJournal of Inequalities and Applications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectMethods
dc.subjectConvergence
dc.subjectSummability
dc.subject47A05
dc.titleGeneral methods of convergence and summability
dc.typeArticle

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