The unit ball of P((2)l(2)(2))

Abstract

We classify extreme points and smooth points of the unit ball of the space P((2)l(2)(2)) Of all 2-homogeneous polynomials on the 2-dimensional real Hilbert space l(2)(2) and show that the unit sphere of P((2)l(2)(2)) is the disjoint union of the set of extreme points of its unit ball and the set of smooth ones We also obtain explicit formulas for the norm of f epsilon P((2)l(p)(2))*(p = 1, 2, infinity).