Infinite-dimensional sets of constant width and their applications.

Angel Rodríguez Palacios

Displaying similar documents to “Infinite-dimensional sets of constant width and their applications.”

Banach spaces which are proper M-ideals

Ehrhard Behrends, Peter Harmand (1985)

Studia Mathematica

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Properly semi-L-embedded complex spaces

Angel Rodríguez Palacios (1993)

Studia Mathematica

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We prove the existence of complex Banach spaces X such that every element F in the bidual X** of X has a unique best approximation π(F) in X, the equality ∥F∥ = ∥π (F)∥ + ∥F - π (F)∥ holds for all F in X**, but the mapping π is not linear.

Transitivity of intersection properties of balls.

Rafael Payá Albert (1986)

Extracta Mathematicae

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On subspaces of Banach spaces where every functional has a unique norm-preserving extension

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...

On Banach spaces which are M-ideals in their biduals.

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...

Containing l or c and best approximation.

Juan Carlos Cabello Piñar (1990)

Collectanea Mathematica

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The purpose of this paper is to obtain sufficient conditions, for a Banach space X to contain or exclude c0 or l1, in terms of the sets of best approximants in X for the elements in the bidual space.

Operators with extension property and the principle of local reflexivity

F. Oertel (1996)

Acta Universitatis Carolinae. Mathematica et Physica

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Banach spaces which are $M$ -ideals in their bidual have property $(u)$

Gilles Godefroy, D. Li (1989)

Annales de l'institut Fourier

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We show that every Banach space which is an $M$ -ideal in its bidual has the property $(u)$ of Pelczynski. Several consequences are mentioned.