Compact and matrix operators on the space $\left\vert A_{f}^{\theta }\right\vert _{k}$

Abstract

In this study, we introduce a new space $\left\vert A_{f}^{\theta}\right\vert_{k}$ by using factorable matrix and investigate its certain topological and algebraic structures where $\theta$ is a positive sequence. Also, we characterize some matrix operators on this space and determine their norms and the Hausdorff measure of noncompactness. In the particular case, we get some well known results.