Spaces of Series Summable by Absolute Cesàro and Matrix Operators

Mehmet Ali Sarıgöl

Abstract


In this paper giving some algebraic and topological properties of \(|C_\alpha|_k\), we characterize the classes of all infinite matrices \((|C_\alpha|,|C_\delta|_k)\) and \((|C_\alpha|_k,|C_\delta|)\) for \(\alpha,\delta>-1\) 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 \(|C_\alpha|_k\) is the space of series summable by absolute Cesaro summability \(|C,\alpha|_k\) in Flett's notation.

Keywords


Summability factors; matrix transformations; sequence spaces; Cesàro spaces

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References


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