On a numerical radius preserving onto isometry on \(\mathcal{L}(X)\) (Q340942)

Let \(X\) be a complex Banach space that is both uniformly convex and uniformly smooth. Let \( {\mathcal L}(X)\) denote the space of bounded linear operators. In this paper the author shows that any numerical radius preserving onto isometry of \({\mathcal L}(X)\) maps the identity operator \(I\) to \(\alpha I\) for some scalar \(\alpha\) with \(|\alpha| = 1\).