Absolutely p-summing operators and Banach spaces containing all uniformly complemented
Andreas Defant (1990)
Studia Mathematica
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Andreas Defant (1990)
Studia Mathematica
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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...
Martin Defant, Marius Junge (1990)
Studia Mathematica
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Reisner, Shlomo (1995)
Serdica Mathematical Journal
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A new, unified presentation of the ideal norms of factorization of operators through Banach lattices and related ideal norms is given.
G. Emmanuele (1993)
Revista Matemática de la Universidad Complutense de Madrid
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We show that a Banach space constructed by Bourgain-Delbaen in 1980 answers a question put by Feder in 1982 about spaces of compact operators.
Catherine Finet (1988)
Studia Mathematica
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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). ...
G. Androulakis (1998)
Studia Mathematica
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Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and...
Józef Banas, Kishin Sadarangani (1995)
Collectanea Mathematica
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The aim of this paper is to discuss the concept of near smoothness in some Banach sequence spaces.
C. Finet, W. Schachermayer (1989)
Studia Mathematica
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V. Montesinos, J. R. Torregrosa (1991)
Collectanea Mathematica
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In this paper we prove that the geometrical notions of Rotundity and Uniform Rotundity of the norm in a Banach space are stable for the generalized Banach products.