Extreme 2-homogeneous polynomials on Hilbert spaces

Abstract

Let H be a (real or complex) Hilbert space. We characterize the extreme points of the unit ball of the space of 2-homogeneous polynomials on H. We find the exact value of the λ-function for P(² H) and thus we show that its unit ball is the norm closed convex hull of its extreme points. We also describe topological properties of the set of extreme points, making connections between the set of extreme points and Grassmanian manifolds.