On the fine spectrum of the operator B(r,s,t) over the sequence spaces ℓp and bvp,(1<p<∞)

Abstract

The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg’s classification of the operator B ( r , s , t ) defined by a triple band matrix over the sequence spaces ℓ p and b v p with 1 < p < ∞ . These results are more general than the spectrum of the second order difference operator Δ 2 and include some other special cases such as the spectrum of the generalized difference operator B ( r , s ) over ℓ p and b v p of Bilgiç and Furkan [H. Bilgiç, H. Furkan, On the fine spectrum of the generalized difference operator B ( r , s ) over the sequence spaces ℓ p and b v p ( 1 < p < ∞ ) , Nonlinear Anal. 68 (3) (2008) 499–506], the spectrum of the difference operator Δ over ℓ p of Akhmedov and Başar [A.M. Akhmedov, F. Başar, On the spectra of the difference operator Δ over the sequence space ℓ p , Demonstratio Math. 39 (3) (2006) 585–595], the spectrum of the same operator over b v p of Akhmedov and Başar [A.M. Akhmedov, F. Başar, On the fine spectra of the difference operator Δ over the sequence space b v p , 1 ⩽ p < ∞ , Acta Math. Sin. Eng. Ser. 23 (10) (2007) 1757–1768], the right shift and Zweier matrices.