On operators factorizable through space
Stanislaw Kwapien (1972)
Mémoires de la Société Mathématique de France
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Stanislaw Kwapien (1972)
Mémoires de la Société Mathématique de France
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F. Oertel (1996)
Acta Universitatis Carolinae. Mathematica et Physica
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F. Oertel (1992)
Acta Universitatis Carolinae. Mathematica et Physica
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Åsvald Lima, Eve Oja (1999)
Studia Mathematica
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We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E). ...
F. Oertel (1995)
Acta Universitatis Carolinae. Mathematica et Physica
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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...
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 .