Banach spaces which are proper M-ideals
Ehrhard Behrends, Peter Harmand (1985)
Studia Mathematica
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Ehrhard Behrends, Peter Harmand (1985)
Studia Mathematica
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Ehrhard Behrends (1988)
Studia Mathematica
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Juan Carlos Cabello Piñar (1990)
Extracta Mathematicae
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A Banach space X is an M-ideal in its bidual if the relation ||f + w|| = ||f|| + ||w|| holds for every f in X* and every w in X ⊥. The class of the Banach spaces which are M-ideals in their biduals, in short, the class of M-embedded spaces, has been carefully investigated, in particular by A. Lima, G. Godefroy and the West Berlin School. The spaces c0(I) -I any set- equipped with their canonical norm belong...
Stanislaw Kwapien (1972)
Mémoires de la Société Mathématique de France
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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...
F. Oertel (1996)
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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