Compact matrix operators on Banach space of absolutely $k$-summable series

Authors: FADİME GÖKÇE

Abstract: In a more recent paper [23], Banach spaces of absolutely $k$-summable series $\left\vert T_{\phi }\right\vert _{k}$ have been introduced and studied by Sarıgöl and Agarwal. In this paper, we characterize matrix and compact operators from the space $\left\vert T_{\phi }\right\vert _{k}$ to the classical spaces $c_{0},c$ and $l_{\infty },$ by determining identities or estimates for operator norms and the Hausdorff measure of noncompactness.

Keywords: Absolute summability, matrix transformations, Hausdorff measure of noncompactness, compact operator, bounded operators, operator norm, sequence spaces

Full Text: PDF