On the compactness and spectra of the generalized difference operator on the spaces ℓ∞ and bv

In this paper, we consider the compactness and the spectrum of the generalized difference operator Δab on the Banach sequence spaces ℓ∞, of bounded sequences, and bv, of bounded variation sequences, which allows us to generalize and extend some existing results for the operator Δab . Furthermore, the results for the operator Δab on ℓ∞ are new even in the case where Δab is reduced to the difference operator Δ . © 2021, Element D.O.O.. All rights reserved.