Resumen de Slices in the unit ball of the symmetric tensor product of C(K)C(K) and L 1(µ)

María Dolores Acosta Vigil, Julio Becerra Guerrero

• We prove that for the cases X=C(K) (K infinite) and X=L1(m) (m s-finite and atomless) it holds that every slice of the unit ball of the N-fold symmetric tensor product of X has diameter two. In fact, we prove more general results for weak neighborhoods relative to the unit ball. As a consequence, we deduce that the spaces of N-homogeneous polynomials on those classical Banach spaces have no points of Fréchet differentiability.