A new double series space derived by factorable matrix and four-dimensional matrix transformations

Abstract

In this study, we introduce a new double series space |F- a,b(u,theta)|(k) using the four dimensional factorable matrix F and absolute summability method for k >= 1. Also, examining some algebraic and topological properties of |F- a,b(u,theta)|(k), we show that it is norm isomorphic to the well-known double sequence space L-k for 1 <= k < infinity. Furthermore, we determine the alpha-, beta (bp)- and gamma-duals of the spaces F|F- a,b(u,theta)|(k) for k >= 1. Additionally, we characterize some new four dimensional matrix transformation classes on double series space |F- a,b(u,theta)|(k). Hence, we extend some important results concerned on Riesz and Cesa`ro a,b matrix methods to double sequences owing to four dimensional factorable matrix.