LAUSR

Abstract We characterize the sets of norm one vectors x 1 , … , x k in a Hilbert space H such that there exists a k-linear symmetric form attaining its norm at ( x 1 , … , x k ) . We prove that in the bilinear case, any two vectors satisfy this property. However, for k ≥ 3 only collinear vectors satisfy this property in the complex case, while in the real case this is equivalent to x 1 , … , x k spanning a subspace of dimension at most 2. We use these results to obtain some applications to symmetric multilinear forms, symmetric tensor products and the exposed points of the unit ball of L s ( H k ) .