On the fine spectrum of the generalized difference operator defined by a double sequential band matrix over the sequence space $ell_p$, (1 < p < ∞)

The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg’s classification of the operator $Binsert ignore into journalissuearticles values(\tilde{r},\tilde{s});$   defined by a double sequential band matrix over the sequence space $\ell_p$  where 1 < p < ∞ . These results are more general than the spectrum of the generalized difference operator B insert ignore into journalissuearticles values( r, s ); over  $\ell_p$  of Bilgiç and Furkan [Nonlinear Anal. 68 insert ignore into journalissuearticles values(3);insert ignore into journalissuearticles values(2008);, 499–506].