The space of compact operators as an M-ideal in its bidual.
T. S. S. R. K. Rao (1992)
Extracta Mathematicae
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T. S. S. R. K. Rao (1992)
Extracta Mathematicae
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Larsen, R. (1971)
Portugaliae mathematica
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Yngve Domar (1982)
Banach Center Publications
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Wolfgang Hensgen (1992)
Collectanea Mathematica
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G. Godefroy, N. Kalton, P. Saphar (1993)
Studia Mathematica
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We show that a Banach space with separable dual can be renormed to satisfy hereditarily an “almost” optimal uniform smoothness condition. The optimal condition occurs when the canonical decomposition is unconditional. Motivated by this result, we define a subspace X of a Banach space Y to be an h-ideal (resp. a u-ideal) if there is an hermitian projection P (resp. a projection P with ∥I-2P∥ = 1) on Y* with kernel . We undertake a general study of h-ideals and u-ideals. For example...
Trond A. Abrahamsen, Asvald Lima, Vegard Lima (2008)
Czechoslovak Mathematical Journal
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Let be a Banach space. We give characterizations of when is a -ideal in for every Banach space in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when is a -ideal in for every Banach space , when is a -ideal in for every Banach space , and when is a -ideal in for every Banach space .
Eve Oja, Märt Põldvere (1996)
Studia Mathematica
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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...
L. Waelbroeck (1983)
Studia Mathematica
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