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 Delta(ab) on the Banach sequence spaces l(infinity), of bounded sequences, and bv, of bounded variation sequences. which allows us to generalize and extend some existing results for the operator Delta(ab) Furthermore, the results for the operator Delta(ab) on l(infinity) are new even in the case where Delta(ab) is reduced to the difference operator Delta.