On the reflexivity of $$\mathcal {P}_{w}(^{n}E;F)$$ |
| |
Authors: | Sergio A Pérez |
| |
Institution: | 1.IMECC, UNICAMP,Campinas,Brazil |
| |
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 \(\mathcal {L}_{K}(E;F)\) 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 \(\mathcal {P}_{w}(^{n}E;F)\) 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|