Displaying similar documents to “Supremum norm differentiability.”

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

Leandro Candido, Elói Medina Galego (2012)

Fundamenta Mathematicae

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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...

Smoothness in Banach spaces. Selected problems.

Marian Fabian, Vicente Montesinos, Václav Zizler (2006)

RACSAM

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This is a short survey on some recent as well as classical results and open problems in smoothness and renormings of Banach spaces. Applications in general topology and nonlinear analysis are considered. A few new results and new proofs are included. An effort has been made that a young researcher may enjoy going through it without any special pre-requisites and get a feeling about this area of Banach space theory. Many open problems of different level of difficulty are discussed. For...

Extremal properties of the set of vector-valued Banach limits

Francisco Javier García-Pacheco (2015)

Open Mathematics

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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...