Spaces of Series Summable by Absolute Cesí ro and Matrix Operators - Sarıgöl, Mehmet Ali (Communications in Mathematics and Applications, 2016)
In this paper giving some algebraic and topological properties of \(|C_α|_k\), we characterize the classes of all infinite matrices \((|C_α|,|C_δ|_k)\) and \((|C_α|_k,|C_δ|)\) for \(α,δ>-1\) and \(k\ge 1\), 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 \(|C_α|_k\) is the space of series summable by absolute Cesaro summability \(|C,α|_k\) in Flett's notation.