On the numerical radius of weighted shift operators with generalized geometric weights

Abstract

In this paper, we give bounds on the numerical radius of the weighted shift operator T with generalized geometric weights$(1,sq,q^2,s{q}^3,\dots ,q^{2n-2},s{q}^{2n-1},\dots ),$ where $s>0$ and $0<q<1$. Also, we provide the entire function $F_T\left(z\right)$ whose minimal positive root gives the numerical radius of the weighted shift operator T. The purpose of this paper is to generalize the results of numerical radius for the weighted shift operator with geometric weights given in [5].