A new conservative matrix derived by Catalan numbers and its matrix domain in the spaces<i>c</i>and<i>c</i>₀

Abstract

The main purpose of this paper is to define a new conservative matrix by means of the fascinating sequence of Catalan numbers and study the matrix domain of this newly introduced matrix in the classical sequence spaces c and c0. Additionally, after determining the Köthe-Toeplitz dual, generalized Köthe-Toeplitz dual and Garling dual, certain matrix transformations and compact operators are characterized on the new Banach spaces.