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

## TL;DR

This paper investigates the reflexivity properties of certain spaces of weakly continuous homogeneous polynomials between reflexive Banach spaces, establishing conditions under which subspaces are reflexive or not isomorphic to dual spaces.

## Contribution

It generalizes previous results and solves a problem posed by Feder regarding the reflexivity of subspaces of polynomial spaces.

## Key findings

- Subspaces are either reflexive or non-isomorphic to dual spaces.
- The result extends Feder's theorem to a broader class of polynomial spaces.
- Provides a characterization of the reflexivity of polynomial subspaces.

## 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}.