On the fine spectrum of the operator B(r,s,t) B ( r , s , t ) over the sequence spaces ?p ? p and bvp,(1<p<?) b v p , ( 1 < p < ? )
The main purpose of this paper is to determine the fine spectrum with respect to the Goldbergs classification of the operator B(r,s,t) B ( r , s , t ) defined by a triple band matrix over the sequence spaces ?p ? p and bvp b v p with 1<p<? 1 < p < ? . These results are more general than the spectrum of the second order difference operator ?2 ? 2 and include some other special cases such as the spectrum of the generalized difference operator B(r,s) B ( r , s ) over ?p ? p and bvp b v p of Bilgi and Furkan [H. Bilgi, H. Furkan, On the fine spectrum of the generalized difference operator B(r,s) B ( r , s ) over the sequence spaces ?p ? p and b v p ( 1 < p < ? ) , Nonlinear Anal. 68 (3) (2008) 499506], the spectrum of the difference operator ? ? over ?p ? p of Akhmedov and Ba?ar [A.M. Akhmedov, F. Ba?ar, On the spectra of the difference operator ? ? over the sequence space ?p ? p , Demonstratio Math. 39 (3) (2006) 585595], the spectrum of the same operator over bvp b v p of Akhmedov and Ba?ar [A.M. Akhmedov, F. Ba?ar, On the fine spectra of the difference operator ? ? over the sequence space bvp,1?p<? b v p , 1 ? p < ? , Acta Math. Sin. Eng. Ser. 23 (10) (2007) 17571768], the right shift and Zweier matrices.
difference operator generalized difference operator spectrum of an operator spectral mapping theorem the sequence spaces ?p ? p and bvp b v p ?p ? p ?p ? p ? p bvp b v p bvp b v p b v p