Karakus, MahmutBasar, Feyzi2024-08-042024-08-0420200022-247X1096-0813https://doi.org/10.1016/j.jmaa.2019.123651https://hdl.handle.net/11616/99083In 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.eninfo:eu-repo/semantics/openAccessAlmost convergencel(infinity)(X)- and c(0)(X)-multiplier convergent seriesContinuity and compactness of summing operatorArticle484110.1016/j.jmaa.2019.1236512-s2.0-85075871465Q1WOS:000508488800018Q1