Subdivision of the Spectra for the Generalized Difference Operator Δ_(a,b) on the Sequence Space l_p " " (1<p<∞)

Abstract

El-Shabrawy has introduced the generalized difference operator denoted by .   Let nonzero real numbers  sequences  and  be convergent sequences such that   and  The generalized difference operator  is  with. In this paper we study the approximate point spectrum, the defect spectrum and the compression spectrum of the operator  on the p-absolutely summable sequences space.

Keywords

• — Generalized difference operator,approximate point spectrum,defect spectrum,compression spectrum

References

1. Yildirim, M. On the spectrum and fine spectrum of the compact Rhaly operators. Indian J. Pure Appl. Math. 1996; 27, 779-784.