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Article Dans Une Revue Annales de l'Institut Fourier Année : 2022

Nonlinear aspects of super weakly compact sets

Résumé

The notion of super weak compactness for subsets of Banach spaces is a strengthening of the weak compactness that can be described as a local version of super-reflexivity. A recent result of K. Tu [34] which establishes that the closed convex hull of a super weakly compact set is super weakly compact has removed the main obstacle to further development of the theory. In this paper we provide a variety of results around super weak compactness in order to show the great scope of this notion. We also give non linear characterizations of super weak compactness in terms of the (non) embeddability of special trees and graphs. We conclude with a few relevant examples of super weakly compact sets in non super-reflexive Banach spaces.
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Dates et versions

hal-03377450 , version 1 (14-10-2021)

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Gilles Lancien, Matias Raja. Nonlinear aspects of super weakly compact sets. Annales de l'Institut Fourier, 2022, 72 (3), pp.1305-1328. ⟨10.5802/aif.3488⟩. ⟨hal-03377450⟩
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