On subspaces of Banach spaces where every functional has a unique norm-preserving extension
Studia Mathematica, Tome 117 (1995) no. 3, pp. 289-306
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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{10_4064_sm_117_3_289_306,
author = {Eve Oja and },
title = {On subspaces of {Banach} spaces where every functional has a unique norm-preserving extension},
journal = {Studia Mathematica},
pages = {289--306},
publisher = {mathdoc},
volume = {117},
number = {3},
year = {1995},
doi = {10.4064/sm-117-3-289-306},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-117-3-289-306/}
}
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%0 Journal Article %A Eve Oja %A %T On subspaces of Banach spaces where every functional has a unique norm-preserving extension %J Studia Mathematica %D 1995 %P 289-306 %V 117 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-117-3-289-306/ %R 10.4064/sm-117-3-289-306 %G en %F 10_4064_sm_117_3_289_306
Eve Oja; . On subspaces of Banach spaces where every functional has a unique norm-preserving extension. Studia Mathematica, Tome 117 (1995) no. 3, pp. 289-306. doi: 10.4064/sm-117-3-289-306
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