Characterizations of some new classes of four-dimensional matrices and dual spaces on the double spaces of Cesàro means

Abstract

The main purpose in this study is to investigate some topological and algebraic properties of the absolutely double series spaces |C_{1,1}|_{k} defined by combining the first order Cesàro means with the concept of absolute summability k≥1. Beside this, we determine the α-dual of the space |C_{1,1}|₁ and the β(bp)- and γ-duals of the spaces |C_{1,1}|_{k} for k≥1. Finally, we characterize some new four-dimensional matrix classes (|C_{1,1}|_{k},υ), (|C_{1,1}|₁,υ), (|C_{1,1}|₁,L_{k}), (|C_{1,1}|_{k},L_{u}), (L_{u},|C_{1,1}|_{k}) and (L_{k},|C_{1,1}|₁), where υ∈{M_{u},C_{bp}} for 1≤k