On the Spectrum of Difference Operator ∆ab Over the Sequence Spaces ℓp and bvp, (1< p<∞)

Abstract: The main purpose of the present paper is to determine the spectrum of the difference operator ∆ab over the sequence spaces ℓp and bvp,(1 < p < ∞). For any two sequences a = (ak) and b = (bk) of distinct, non zero real numbers and satisfying certain conditions, the difference operator ∆ab is defined by (∆abx)k = akxk+ bk−1xk−1, where (xk) ∈ ℓp or bvp and x−1 = 0. Finally, we obtain the spectrum, point spectrum, residual spectrum and the continuous spectrum of the difference operator ∆ab over ℓp and bvp