Separated sequences in uniformly convex Banach spaces

• Autorzy: J. M. A. M. van Neerven
• Języki publikacji: EN

Abstrakty

EN

We give a characterization of uniformly convex Banach spaces in terms of a uniform version of the Kadec-Klee property. As an application we prove that if (xₙ) is a bounded sequence in a uniformly convex Banach space X which is ε-separated for some 0 < ε ≤ 2, then for all norm one vectors x ∈ X there exists a subsequence $(x_{n_j})$ of (xₙ) such that
$inf_{j≠k} ||x -(x_{n_j} - x_{n_k})|| ≥ 1 + δ_X(2/3 ε)$,
where $δ_X$ is the modulus of convexity of X. From this we deduce that the unit sphere of every infinite-dimensional uniformly convex Banach space contains a $(1+ 1/2 δ_X(2/3))$-separated sequence.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 102
• Numer: 1
• Strony: 147-153

Daty

wydano

2005

Twórcy

autor

J. M. A. M. van Neerven

• Delft Institute of Applied Mathematics, Technical University of Delft, P.O. Box 5031, 2600 GA Delft, The Netherlands

Identyfikatory

DOI

10.4064/cm102-1-13