Operator valued series, almost summability of vector valued multipliers and (weak) compactness of summing operator

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dc.authoridKarakuş, Mahmut/0000-0002-4468-629X
dc.authorwosidKarakuş, Mahmut/HHY-8747-2022
dc.contributor.authorKarakus, Mahmut
dc.contributor.authorBasar, Feyzi
dc.date.accessioned2024-08-04T20:46:58Z
dc.date.available2024-08-04T20:46:58Z
dc.date.issued2020
dc.departmentİnönü Üniversitesien_US
dc.description.abstractIn this study, we introduce the vector valued multiplier spaces M-f(infinity)(Sigma T-k(k) ) and M-wf(infinity)(Sigma(k) T-k) by means of almost summability and weak almost summability, and a series of bounded linear operators. Since these multiplier spaces are equipped with the sup norm and are subspaces of l(infinity) (X), we obtain the completeness of a normed space via the multiplier spaces which are complete for every c(0) (X)-multiplier Cauchy series. We also characterize the continuity and (weakly) compactness of the summing operator S from the multiplier spaces M-f(infinity)(Sigma T-k(k) ) or M-wf(infinity)(Sigma(k) T-k) to an arbitrary normed space Y through c(0) (X)-multiplier Cauchy and too (X)-multiplier convergent series, respectively. Finally, we show that if Sigma(k) T-k is l(infinity) (X)-multiplier Cauchy, then the multiplier spaces of almost convergence and weak almost convergence are identical. These results are more general than the corresponding consequences given by Swartz [20], and are analogues given by Altay and Kama [6]. (C) 2019 Published by Elsevier Inc.en_US
dc.identifier.doi10.1016/j.jmaa.2019.123651
dc.identifier.issn0022-247X
dc.identifier.issn1096-0813
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85075871465en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.1016/j.jmaa.2019.123651
dc.identifier.urihttps://hdl.handle.net/11616/99083
dc.identifier.volume484en_US
dc.identifier.wosWOS:000508488800018en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherAcademic Press Inc Elsevier Scienceen_US
dc.relation.ispartofJournal of Mathematical Analysis and Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectAlmost convergenceen_US
dc.subjectl(infinity)(X)- and c(0)(X)-multiplier convergent seriesen_US
dc.subjectContinuity and compactness of summing operatoren_US
dc.titleOperator valued series, almost summability of vector valued multipliers and (weak) compactness of summing operatoren_US
dc.typeArticleen_US

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