Compact operators on the Motzkin sequence space $c_0(\mathcal{M})$

Abstract

The concept of non-compactness measure is extremely beneficial for functional analysis in theories, such as fixed point and operator equations. Apart from these, the Hausdorff measure of non-compactness also has some applications in the theory of sequence spaces which is an interesting topic of functional analysis. One of these applications is to obtain necessary and sufficient conditions for the matrix operators between Banach coordinate (BK) spaces to be compact. In line with these explanations, in this study, the necessary and sufficient conditions for a matrix operator to be compact from the Motzkin sequence space $c_0(\mathcal{M})$ to the sequence space $\mu\in\{\ell_{\infty},c,c_0,\ell_1\}$ are presented by using Hausdorff measure of non-compactness.