Compactness criteria and spectra of some infinite lower triangular matrices

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