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.
@article{bwmeta1.element.bwnjournal-article-smv117i3p289bwm,
author = {Eve Oja and M\"art P\~oldvere},
title = {On subspaces of Banach spaces where every functional has a unique norm-preserving extension},
journal = {Studia Mathematica},
volume = {119},
year = {1996},
pages = {289-306},
zbl = {0854.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv117i3p289bwm}
}
Oja, Eve; Põldvere, Märt. On subspaces of Banach spaces where every functional has a unique norm-preserving extension. Studia Mathematica, Tome 119 (1996) pp. 289-306. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv117i3p289bwm/
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