On the fine spectrum of the operator B(r, s, t) over the sequence spaces l(p) and bv(p), (1 < p < infinity)
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 bv(p) with 1 < p < infinity. These results are more general than the spectrum of the second order difference operator Delta(2) and include some other special cases such as the spectrum of the generalized difference operator B(r, s) over l(p) and bv(p) of Bilgic and Furkan [H. Bilgic, H. Furkan, On the fine spectrum of the generalized difference operator B(r, s) over the sequence spaces l(p) and bv(p) (1 < p < infinity), Nonlinear Anal. 68 (3) (2008)499-506], the spectrum of the difference operator Delta over l(p) of Akhmedov and Basar [A.M. Akhmedov, F. Basar, On the spectra of the difference operator Delta over the sequence space l(p), Demonstratio Math. 39 (3) (2006) 585-595], the spectrum of the same operator over bv(p) of Akhmedov and Basar [A.M. Akhmedov, F. Basar, On the fine spectra of the difference operator Delta over the sequence space bv(p). 1 <= p <= infinity, Acta Math. Sin. Eng. Ser. 23 (10)(2007) 1757-1768], the right shift and Zweier matrices. Published by Elsevier Ltd
the sequence spaces l(p) and bv(p) difference operator generalized difference operator spectrum of an operator spectral mapping theorem