The spectrum of the generalized difference operator B _v^(m) over the sequence space ℓ_p (1 < p < ∞

In this paper, we determine the spectrum, the point spectrum, the residual spectrum and the continuous spectrum of the operator (Formula presented.) on the sequence space (Formula presented.) (Formula presented.). These results generalize the spectrum of the difference operator (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) and some other cases (Formula presented.), (Formula presented.), (Formula presented.) over the space (Formula presented.).