Symmetric multilinear forms on Hilbert spaces: where do they attain their norm?

Daniel Carando, Jorge Tomás Rodríguez

We characterize the sets of norm one vectors ${\mathbf{x}}_1,\dots ,{\mathbf{x}}_k$ in a Hilbert space $\mathcal{H}$ such that there exists a $k$-linear symmetric form attaining its nor…