Spaces of Series Summable by Absolute Cesaro and Matrix Operators

Abstract

In this paper giving some algebraic and topological properties of vertical bar C-alpha vertical bar(k), we characterize the classes of all infinite matrices (vertical bar C-alpha vertical bar, vertical bar C-delta vertical bar(k)) and (vertical bar C-alpha vertical bar(k), vertical bar C-delta vertical bar) for alpha, delta > -1 and k >= 1, show that each element of this classes correspond to a continuous linear mapping, which also enables us to extend some well known results of Flett [7], Orhan and Sarigol [15], Bosanquet [2], Mehdi [13], Mazhar [11], and Sarigol [18], where vertical bar C-alpha vertical bar(k) is the space of series summable by absolute Cesaro summability vertical bar C, alpha vertical bar(k) in Flett's notation.