### Subdivisions of the Spectra for Generalized Difference Operator over Certain Sequence Spaces

#### Abstract

The fine spectrum of the generalized difference operator B(r, s) represented by a double band matrix over the sequence spaces c0 and c was studied by Altay and Basar [B. Altay, F. Basar, On the fine spectrum of the generalized difference operator B(r, s) over the sequence spaces c0 and c, Int. J. Math. Math. Sci. 2005 (18) (2005) 3005–3013], over the sequence spaces ℓp and bvp was worked by Bilgic and Furkan [H. Bilgic, H. Furkan, On the fine spectrum of the generalized difference operator B(r, s) over the sequence spaces ℓp and bvp, (1 < p < ∞), Nonlinear Anal. 68 (3) (2008) 499–506]; where bvp denotes the space of all sequences (xk) such that (xk − xk−1) in ℓp with 1 < p < ∞ and was studied by Basar and Altay [F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian Math. J. 55 (1) (2003) 136–147]. In this paper, the approximate point spectrum, defect spectrum and compression spectrum of the generalized difference operator B(r, s) over the sequence spaces c0, c, ℓp and bvp have been determined.

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