A Note On The Matrix Operators Of Absolute Nörlund Series Space

Abstract

On the recent study, the series space $\left\vert N_{p}^{\theta }\right\vert (q )$ has been introduced as the set of all series summable by the absolute Nörlund summability method, which includes the Maddox's space $l(q )$, the absolute Cesaro space $\left\vert C_{\alpha }\right\vert _{k}$ and the absolute Nörlund space $\left\vertN_{p}^{\theta }\right\vert _{k}$, and studied in terms of some topological and algebraic properties and matrix transformations by Gökçe and Sarıgöl. In this paper, some characterizations of matrix operators between the absolute Nörlund series space $\left\vert N_{p}^{\theta }\right\vert (q )$ and the classical sequence spaces $c,c_0,l_{\infty}$ are given. Also, it is shown that the matrix operators are bounded operators. Finally, certain results are obtained as a special case.

Keywords

• Nörlund means;
• matrix transformation;
• bounded linear operator;
• Maddox’s space.

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