On the reflexivity of $\mathcal{P}_{w}(^{n}E;F)$

Abstract

In this paper we prove that if $E$ and $F$ are reflexive Banach spaces and $G$ is a closed linear subspace of the space $\mathcal{P}_{w}(^{n}E;F)$ of all $n$-homogeneous polynomials from $E$ to $F$ which are weakly continuous on bounded sets, then $G$ is either reflexive or non-isomorphic to a dual space. This result generalizes \cite[Theorem 2]{FEDER} and gives the solution to a problem posed by Feder \cite[Problem 1]{FED}.