Vector valued multiplier spaces of f?-summability, completeness through c0(X)-multiplier convergence and continuity and compactness of summing operators

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dc.authoridKarakuş, Mahmut/0000-0002-4468-629X
dc.authoridBasar, Feyzi/0000-0002-9949-1481
dc.authorwosidKarakuş, Mahmut/HHY-8747-2022
dc.contributor.authorKarakus, Mahmut
dc.contributor.authorBasar, Feyzi
dc.date.accessioned2024-08-04T20:48:44Z
dc.date.available2024-08-04T20:48:44Z
dc.date.issued2020
dc.departmentİnönü Üniversitesien_US
dc.description.abstractQuite recently, the authors introduced the vector valued multiplier spaces associated to the series of bounded linear operators M-f(infinity)(Sigma(k) T-k) and M-wf(infinity)(Sigma(k) T-k) by means of almost and weak almost summability, respectively; [J. Math. Anal. Appl. 484: 123651]. As was recorded as an open problem in [J. Math. Anal. Appl. 484: 123651], in this study, we introduce vector valued multiplier spaces M-f lambda(infinity)(Sigma(k) T-k) and M-wf lambda(infinity)(Sigma(k) T-k) by means of generalized almost and weak almost summability, and give a characterization of completeness of these spaces, via c(0)(X)-multiplier convergent series. We also characterize the continuity and the (weak) compactness of the summing operator S from the multiplier spaces M-f lambda(infinity)(Sigma(k) T-k) or M-wf lambda(infinity)(Sigma(k) T-k) to an arbitrary normed space Y through c(0)(X)-multiplier Cauchy and l(infinity)(X)-multiplier convergent series, respectively. Finally, we prove that if Sigma(k) T-k is l(infinity)(X)-multiplier Cauchy, then the spaces M-f lambda(infinity)(Sigma(k) T-k) and M-wf lambda(infinity)(Sigma(k) T-k) are identical. These results are more general than the corresponding consequences given in [J. Math. Anal. Appl. 484: 123651] since almost convergence can be obtained from f(lambda) -convergence under certain conditions.en_US
dc.identifier.doi10.1007/s13398-020-00898-0
dc.identifier.issn1578-7303
dc.identifier.issn1579-1505
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85087939516en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.1007/s13398-020-00898-0
dc.identifier.urihttps://hdl.handle.net/11616/99415
dc.identifier.volume114en_US
dc.identifier.wosWOS:000548645900001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringer-Verlag Italia Srlen_US
dc.relation.ispartofRevista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicasen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectAlmost summabilityen_US
dc.subjectc(0)(X)- and l(infinity)(X)-multiplier convergent seriesen_US
dc.subjectCompletenessen_US
dc.titleVector valued multiplier spaces of f?-summability, completeness through c0(X)-multiplier convergence and continuity and compactness of summing operatorsen_US
dc.typeArticleen_US

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