Unitary similarity and the numerical radius preservers

Abstract

Let $B\left(H\right)$ be the algebra of all bounded linear operators acting on a separable infinite-dimensional complex Hilbert space $H$, and denote by $w\left(T\right)$ the numerical radius of any operator $T\in B\left(H\right)$. In this paper, we describe the form of all bijective linear maps ϕ on $B\left(H\right)$ for which $w\left(\varphi \right(T\left)\right)=w\left(\varphi \right(S\left)\right)$ whenever $T,S\in B\left(H\right)$ are two unitarily similar operators.