Asymptotic smoothness, concentration properties in Banach spaces and applications

Fovelle, Audrey

doi:10.1016/j.jfa.2024.110763

2311.15900v2.pdf (191.0Ko)

Identificadores

URI: https://hdl.handle.net/10481/102399

DOI: 10.1016/j.jfa.2024.110763

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Editorial

Elsevier

Materia

Banach spaces

Hamming graphs

Asymptotic smoothness

Nonlinear embeddings

Concentration properties

Date

2024-11-20

Referencia bibliográfica

Published version: Fovelle, Audrey. Journal of Functional Analysis Volume 288, Issue 4, 15 February 2025, 110763. https://doi.org/10.1016/j.jfa.2024.110763

Patrocinador

MCIN/AEI/10.13039/501100011033 PID2021-122126NBC31, CEX2020-001105-M

Résumé

We prove an optimal result of stability under ℓp-sums of some concentration properties for Lipschitz maps defined on Hamming graphs into Banach spaces. As an application, we give examples of spaces with Szlenk index arbitrarily high that admit nevertheless a concentration property. In particular, we get the very first examples of Banach spaces with concentration but without asymptotic smoothness property.

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