Abstract
The generalized difference operator Delta(a,b) on the sequence space l(p) is defined by Delta(a,b) x = Delta(a,b) (x(k)) = (a(k)x(k) + b(k-1)x(k-1))(k=0)(infinity) with x(-1) = 0, where (a(k)) and (b(k)) are two convergent sequences of nonzero real numbers satisfying certain conditions. It is the purpose of this paper to completely determine the spectrum, the point spectrum, the residual spectrum and the continuous spectrum of the operator Delta(a,b) on the sequence space l(p), where 1 < p < infinity.