A New Paranormed Series Space and Matrix Transformations

Abstract

The series space |C-1|p has been studied for 1 < p < ∞ by Hazar and Sarigöl in [9]. The main purpose of this work is to define a new paranormed space |C-1| (p), where p = (pk) is a bounded sequence of positive real numbers, which generalizes the results of Hazar and Sangöl 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. © 2020, Murat TOSUN. All rights reserved.