A New Paranormed Series Space and Matrix Transformations

Abstract

The series space |C−1|phas been studied for 1 ≤ p < ∞ by Hazar and Sarıgöl in [9]. The main purposeof this work is to define a new paranormed space |C−1|(p), where p = (pk) is a bounded sequence ofpositive real numbers, which generalizes the results of Hazar and Sarıgöl in [9] to paranormed space.Also, we investigate some topological properties such as the completeness and the isomorphism, and wedetermine the α−, β−, and γ duals of this paranormed space. Additionally, we give characterization ofthe classes of infinite matrices (|C−1|(p), µ) and (µ, |C−1|(p)), where µ is any given sequence space.