Spectral Properties of the Compact Rhaly and Compact Generalised Ces{à}ro Operators on Weighted $c_0$ Spaces

Abstract

In this article, we conduct a comprehensive study on the continuity, compactness, and spectral properties of Rhaly operators and generalized Cesàro operators, acting on weighted null sequence spaces. We determine the point spectrum, continuous spectrum, and residual spectrum for compact Rhaly operators and compact generalized Cesàro operators. Additionally, we explore Goldberg's classifications of Rhaly operators over weighted null sequence spaces.