A New Paranormed Series Space and Matrix Transformations

Abstract

The series space |C −1 | p has been studied for 1 ≤ p < ∞ by Hazar and Sarıgöl in [9]. The main purpose of this work is to define a new paranormed space |C −1 | (p), where p = (p k) is a bounded sequence of positive 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 we determine the α−, β−, and γ duals of this paranormed space. Additionally, we give characterization of the classes of infinite matrices (|C −1 | (p), µ) and (µ, |C −1 | (p)), where µ is any given sequence space.