On the reflexivity of P_w(nE;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 𝐾(𝐸;𝐹) of all compact linear operators from E into F, then G is either reflexive or non-isomorphic to a dual space. This result generalizes (Israel J Math 21:38-49, 1975, Theorem 2) and gives the solution to a problem posed by Feder (Ill J Math 24:196-205, 1980, Problem 1). We also prove that if E and F are reflexive Banach spaces, then the space 𝑤(𝑛𝐸;𝐹) of all n-homogeneous polynomials from E into F which are weakly continuous on bounded sets is either reflexive or non-isomorphic to a dual space.

Sergio A. Pérez

Instructor