Conjugations of Unitary Operators, II

Abstract

For a given unitary operator $U$ on a separable complex Hilbert space $\h$, we describe the set ${\mathcal{C}}_c(U)$ of all conjugations $C$ (antilinear, isometric, and involutive maps) on $\h$ for which $CUC=U$. As this set might be empty, we also show that ${\mathcal{C}}_c(U)\ne \varnothing$ if and only if $U$ is unitarily equivalent to $U^{\ast }$.