Compactness criteria and spectra of some infinite lower triangular matrices

Abstract

In this paper, a study is made on two well-known operator matrices; the Rhaly operator Ra and the generalized difference operator ?ab. Firstly, some compactness results for the operators Ra and ?ab, whose purpose is to help in describing their spectra, are derived. Next, general results on investigating the spectra of such operators on a large class of Banach sequence spaces are established. These results give a complete description of the spectra. The obtained results unify, extend and improve many comparable results in the existing literature.