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.
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S. Pérez was supported by CAPES and CNPq, Brazil.
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Pérez, S.A. On the reflexivity of \(\mathcal {P}_{w}(^{n}E;F)\) . Arch. Math. 109, 471–475 (2017). https://doi.org/10.1007/s00013-017-1084-6
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DOI: https://doi.org/10.1007/s00013-017-1084-6