Some Spectral Properties of the Generalized Difference Operator (Delta)v

Abstract

In this paper we consider the generalized difference operator

 

v on the sequence spaces l1 and c0. The operator v is represented by a lower triangular double band matrix whose nonzero entries are the elements of a sequence (vk) with certain conditions. We mainly review several recent results concerning the fine spectrum of the operatorv over the equence spaces l1 and c0. Also, we provide some new results. Following that we give some illustrative examples which motivate the main results. Finally, we give notes on the fine spectrum of the operator v . These notes attempt to present some ideas about changing the conditions on the sequence (vk) in the fine spectrum of the operatorv . The new results of this paper generalize and improve some recent results that appeared recently in the literature.