On the numerical radius of a class of weighted shift operators

Abstract: In this paper, we derive some bounds on numerical radius of the weighted shift operator $T$ with weights $$(1,sq,q<sup>2,tq<sup>3,q<sup>4,sq<sup>5,q<sup>6,tq<sup>7,\ldots)$$ where $s,t &gt;0$ and $0<q<1$. Furthermore, we provide an entire function $F_T(z)$. The reciprocal of the minimal positive root of $F_T(z)=0$ gives the numerical radius of $T$. These results generalize several previously known results on the numerical radius of weighted shift operators discussed in \cite{chakraborty2025numerical}.