Displaying similar documents to “On Kottman's constants in Banach spaces”

How far is C₀(Γ,X) with Γ discrete from C₀(K,X) spaces?

Leandro Candido, Elói Medina Galego (2012)

Fundamenta Mathematicae

Similarity:

For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the...

Product spaces generated by bilinear maps and duality

Enrique A. Sánchez Pérez (2015)

Czechoslovak Mathematical Journal

Similarity:

In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding...

More lr saturated L∞ spaces

Gasparis, I., Papadiamantis, M. K., Zisimopoulou, D. Z. (2010)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 05D10, 46B03. Given r ∈ (1, ∞), we construct a new L∞ separable Banach space which is lr saturated.

Lipschitz-free Banach spaces

G. Godefroy, N. J. Kalton (2003)

Studia Mathematica

Similarity:

We show that when a linear quotient map to a separable Banach space X has a Lipschitz right inverse, then it has a linear right inverse. If a separable space X embeds isometrically into a Banach space Y, then Y contains an isometric linear copy of X. This is false for every nonseparable weakly compactly generated Banach space X. Canonical examples of nonseparable Banach spaces which are Lipschitz isomorphic but not linearly isomorphic are constructed. If a Banach space X has the bounded...

Extremal properties of the set of vector-valued Banach limits

Francisco Javier García-Pacheco (2015)

Open Mathematics

Similarity:

In this manuscript we find another class of real Banach spaces which admit vector-valued Banach limits different from the classes found in [6, 7]. We also characterize the separating subsets of ℓ∞(X). For this we first need to study when the space of almost convergent sequences is closed in the space of bounded sequences, which turns out to happen only when the underlying space is complete. Finally, a study on the extremal structure of the set of vector-valued Banach limits is conducted...