GEOMETRY OF SPACES OF POLYNOMIALS

Connections between the shape of the unit ball of a Banach space and a nalytic properties of the Banach space have been studied for many year s. Ln this article, some geometric properties of spaces related to n-h omogeneous polynomials are considered. In particular, the rotundity an d smoothness of spaces of continuous It-homogeneous polynomials and it s preduals are studied. Furthermore, an inequality relating the produc t of the norms of linear functionals on a Banach space with the norm o f the continuous n-homogeneous polynomial determined by the product of the linear functionals is derived. This inequality is used to study t he strongly exposed points of the predual of the space of continuous 2 -homogeneous polynomials. (C) 1998 Academic Press.