Multiplication operator on weighted Lebesgue sequence spaces

Abstract

In this paper, we study the multiplication operator acting on the Lebesgue sequence space l_{p, w}, for 1 ≤ p ≤ ∞, which generalizes the classical l_p spaces by incorporating a weight sequence w_n. We focus on properties such as continuity, inverse continuity, finite range, compactness, and essential norm of the operator.