Some Spectral Aspects of the Operator over the Sequence Spaces and

Abstract

The main idea of the present paper is to compute the spectrum and the fine spectrum of the generalized difference operator over the sequence spaces . The operator denotes a triangular sequential band matrix defined by with for , where or , ; the set nonnegative integers and is either a constant or strictly decreasing sequence of positive real numbers satisfying certain conditions. Finally, we obtain the spectrum, the point spectrum, the residual spectrum, and the continuous spectrum of the operator over the sequence spaces and . These results are more general and comprehensive than the spectrum of the difference operators , , , , and and include some other special cases such as the spectrum of the operators , , and over the sequence spaces or .

On the Spectral Properties of the Weighted Mean Difference Operator Gu,v;Δ over the Sequence Space ℓ1Baliarsingh1, Dutta2 2014International Journal of AnalysisSelf Cite0000View full textAdd to dashboardCite

“…The fine spectrum of the generalized difference operators ( , ) and ( , , ) over the sequence spaces ℓ , V and ℓ 1 , V has been studied by Bilgiç and Furkan [11,12], respectively. Recently, the spectrum of some particular limitation matrices in certain sequence spaces has been studied by [13][14][15] and many others.…”