A remark on the spectrum of fractional difference operator

Abstract

This work computes the spectrum of the backward fractional difference operator over various Banach spaces and . Note that recently, the spectrum of the fractional difference operator , ( being either a constant or strictly decreasing sequence of positive real numbers satisfying some conditions) on the sequence space has been computed by Baliarsingh P. [On the spectrum of fractional difference operator. Linear Multilinear Algebra. 2021;1–13] and it has been noticed that the results obtained are unified and more general, but lack of accuracy for the case . In this work, we improve the results by providing the sharper estimations and some illustrative examples. Also, individual sets describing the point, the residual and the continuous spectrum of the operator on the Banach space c and are computed.