A study on Spectrum classification of the operator D(p,0,0,q) over Hahn Sequence Space h

Abstract

The Hahn sequence space is defined as $h=\left\lbrace y=(y_n)\in w:\sum_{k=1}^{\infty}k|\triangle y_k|<\infty ~and~ \lim_{k\rightarrow\infty}y_k=0\right\rbrace$, where $\triangle y_k=y_k-y_{k+1}$, for all $k\in N.$ In this paper we study the spectrum and fine spectrum of the difference operator $D(p, 0, 0, q)$ over the Hahn sequence space $h$. Further, we subdivide the spectrum into the approximate point spectrum, the defect spectrum and the compression spectrum.