Weak sequential completeness of spaces of homogeneous polynomials

Let Pw(En;F) be the space of all continuous n-homogeneous polynomials from a Banach space E into another F  , that are weakly continuous on bounded sets. We give sufficient conditions for the weak sequential completeness of Pw(En;F). These sufficient conditions are also necessary if both E⁎E⁎ and F   have the bounded compact approximation property. We also show that the weak sequential completeness and the reflexivity of Pw(En;F) are equivalent whenever both E and F are reflexive.