Isomorphisms between spaces of multilinear mappings or homogeneous polynomials

Abstract

Let and be Banach spaces. Ourobjective in this  work is to find conditions under which,whenever the topological dual spaces and are isomorphic,the spaces of multilinear mappings (resp. homogeneous polynomials)on and are isomorphic as well. We also examine  thecorresponding problem for the spaces of multilinear mappings(resp. homogeneous polynomials) of a certain type, for instance offinite, nuclear, compact or weakly compact type.