Generalization of the Absolute Cesàro Space and Some Matrix Transformations

Abstract

The space was extended to the space by Maddox, where is a bounded sequence of positive numbers. The series space has more recently been studied by Hazar and Sarıgöl. In this article, following Maddox we derived a more general series space and show that it is a paranormed space and linearly isomorphic to the space Also, we construct its duals and Schauder basis. Further, we characterize the classes of certain matrix transformations on that space and obtain some well-known results as a particular case.