Isomorphisms between spaces of multilinear mappings or homogeneous polynomials

Let $E$ and $F$ be Banach spaces. Ourobjective in this work is to find conditions under which,whenever the topological dual spaces $E'$ and $F'$ are isomorphic,the spaces of multilinear mappings (resp. homogeneous polynomials)on $E$ and $F$ 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