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

Authors : Feyzi BAŞAR, Ali KARAİSA

Pages : 1315-1332

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Publication Date : 2015-12-01

Article Type : Research Paper

Abstract :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]. 
Keywords : Spectrum of an operator, double sequential band matrix, spectral mapping theorem, the sequence space lp, Goldbergs classification