Abstract
In this study, we deal with some new vector valued multiplier spaces S_{G_{h}}(sum_{k}z_{k}) and S_{wG_{h}}(sum_{k}z_{k}) related with sum_{k}z_{k} in a normed space Y. Further, we obtain the completeness of these spaces via weakly unconditionally Cauchy series in Y and Y^{*}. Moreover, we show that if sum_{k}z_{k} is unconditionally Cauchy in Y, then the multiplier spaces of G_{h}-almost convergence and weakly G_{h}-almost convergence are identical. Finally, some applications of the Orlicz–Pettis theorem with the newly formed sequence spaces and unconditionally Cauchy series sum_{k}z_{k} in Y are given.
Highlights
Introduction and preliminariesConsider as the space of real valued sequences
K zk is wuC iff k |z∗(zk)| < ∞ ∀z∗ ∈ Y ∗, the space of all linear and bounded functionals defined on Y
Corollary 3.3 Let Y be the Banach space such that the formal series k zk belongs to Y
Summary
Introduction and preliminariesConsider as the space of real (or complex) valued sequences. For a detailed study about the difference sequence spaces, one can refer to [27, 28]. K zk is wuC iff k |z∗(zk)| < ∞ ∀z∗ ∈ Y ∗, the space of all linear and bounded (continuous) functionals defined on Y .
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