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 Ces`aro operators, acting on weighted null sequence spaces. We determine the point spectrum, continuous spectrum, and residual spectrum for compact Rhaly operators and compact generalized Ces`aro operators. Additionally, we explore Goldberg's classifications of Rhaly operators over weighted null sequence spaces.