Displaying similar documents to “Properly semi-L-embedded complex spaces”

Infinite-dimensional sets of constant width and their applications.

Angel Rodríguez Palacios (1990)

Extracta Mathematicae

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Sets of constant width appear as a curiosity in the context of finite-dimensional Euclidean spaces. These sets are convex bodies of such an space with the property that the distance between any two distinct parallel supporting hyperplanes is constant. The easiest example of a set of constant width which is not a ball is the so called Reuleaux triangle in the Euclidean plane. This is the intersection of three closed discs of radius r, whose centers are the vertices of an equilateral triangle...

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.

Topological tensor products of a Fréchet-Schwartz space and a Banach space

Alfredo Peris (1993)

Studia Mathematica

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We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that E ⊗ ε X is not an inductive limit of normed spaces for some Banach space X. This solves in the negative open questions of Bierstedt, Meise and Hollstein. As a consequence we obtain Fréchet-Schwartz spaces F and Banach spaces X such that the problem of topologies of Grothendieck has a negative answer for F ⨶ π X . This solves in the negative a question of Taskinen....

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...

Extremely non-complex Banach spaces

Miguel Martín, Javier Merí (2011)

Open Mathematics

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A Banach space X is said to be an extremely non-complex space if the norm equality ∥Id +T 2∥ = 1+∥T 2∥ holds for every bounded linear operator T on X. We show that every extremely non-complex Banach space has positive numerical index, it does not have an unconditional basis and that the infimum of diameters of the slices of its unit ball is positive.