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 Başar [B. Altay, F. Başar, 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 ?p and bvp was worked by Bilgiç and Furkan [H. Bilgiç, H. Furkan, On the fine spectrum of the generalized difference operator B(r, s) over the sequence spaces ?p and bvp, (1 lt; p lt; ?), Nonlinear Anal. 68 (3) (2008) 499-506]; where bvp denotes the space of all sequences (xk) such that (xk - xk-1) in ?p with 1 lt; p lt; ? and was studied by Bas ?ar and Altay [F. Başar, 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, ?p and bvp have been determined. © 2011 by the Mathematical Association of Thailand. All rights reserved.