NOTES ON THE SPECTRAL PROPERTIES OF THE WEIGHTED MEAN DIFFERENCE OPERATOR G (u, v; Δ) OVER THE SEQUENCE SPACE l1

Abstract

In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014(2014), Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G (u, v; Delta) over the sequence space l(1). The product operator G (u, v; Delta) over l(1) is defined by (G (u, v; Delta) x)(k) = Sigma(k)(i=0)u(k)v(i) (x(i)-x(i-1)) with x(k) = 0 for all k < 0, where x = (x(k)) is an element of l(1) and u and v are either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G (u, v; Delta) on the sequence space l(1).