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 ??, ??, and ? 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.