Weakly invariant norms: geometry of spheres in the space of skew-Hermitian matrices

Gabriel Larotonda, Iván Rey

Let $N$ be a weakly unitarily invariant norm (i.e. invariant for the coadjoint action of the unitary group) in the space of skew-Hermitian matrices ${\mathfrak{u}}_n(\mathbb{C})$. In…