Matrix transformations and compact operators on Catalan sequence spaces

Abstract This paper is devoted to the study of domain of a recently defined conservative matrix in the spaces of p-absolutely summable sequences and bounded sequences. The aforementioned matrix is obtained by using the fascinating Catalan numbers. After determining the β-duals of the newly defined Banach spaces, the characterization of some matrix operators are obtained. Finally, the characterization of certain compact operators is presented by utilizing the Hausdorff measure of non-compactness.

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