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Title

On subspaces of Banach spaces where every functional has a unique norm-preserving extension

Authors 1, 2

Affiliations

  1. Institute of Pure Mathematics, Tartu University, Vanemuise 46, EE-2400 Tartu, Estonia
  2. nstitute of Pure Mathematics, Tartu University, Vanemuise 46, EE-2400 Tartu, Estonia

Abstract

Let X be a Banach space and Y a closed subspace. We obtain simple geometric characterizations of Phelps' property U for Y in X (that every continuous linear functional g ∈ Y* has a unique norm-preserving extension f ∈ X*), which do not use the dual space X*. This enables us to give an intrinsic geometric characterization of preduals of strictly convex spaces close to the Beauzamy-Maurey-Lima-Uttersrud criterion of smoothness. This also enables us to prove that the U-property of the subspace K(E,F) of compact operators from a Banach space E to a Banach space F in the corresponding space L(E,F) of all operators implies the U-property for F in F** whenever F is isomorphic to a quotient space of E.

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Studia Mathematica
1995-1996/117/3
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Pages:
289-306
Main language of publication
English
Received
1995-07-12
Accepted
1995-09-11
Published
1996
Exact and natural sciences