CANONICAL ISOMETRIES BETWEEN SPACES OF POLYNOMIALS

Silvia Lassalle

Abstract: This talk is concerned with work with Christopher Boyd in which isometries between spaces of homogeneous polynomials are studied. We characterize the case of P_{A}(^{n}E) when E is a real Banach space. In the complex case a better knowledge of the extreme points of the unit ball of P_{I}(^{n}E) is required. The characterization of the isometries of P_{A}(^{n}E) when E is a real Banach space can be extended to give a characterization of the isometries of P_{A}(^{n}E, X) where X is a Banach space with X′ strictly convex. This result replies heavily on the idea of centralizer of a Banach space.