Grecu, B.C.Muñoz-Fernández, Gustavo A.Seoane Sepúlveda, Juan Benigno2023-06-202023-06-2020090025-587410.1007/s00209-008-0438-yhttps://hdl.handle.net/20.500.14352/50167Let H be a two-dimensional complex Hilbert space and P(H-3) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, B-P(3H), from which we deduce that the unit sphere of P(H-3) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of B-P(3H) remains extreme as considered as an element of B-L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(H-3) and give a characterization of its smooth points.engjournal articlehttp://www.springerlink.comrestricted access517.98Unconditional constantPolynomial inequalitiesTrinomialsHomogeneous polynomialsExtreme pointsAnálisis funcional y teoría de operadores