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Article Dans Une Revue Banach Journal of Mathematical Analysis Année : 2021

On the Weak Maximizing Properties

Résumé

Quite recently, a new property related to norm-attaining operators has been introduced: the weak maximizing property (WMP). In this note, we define a generalised version of it considering other topologies than the weak one (mainly the weak * topology). We provide new sufficient conditions, based on the moduli of asymptotic uniform smoothness and convexity, which imply that a pair (X, Y) enjoys a certain maximizing property. This approach not only allows us to (re)obtain as a direct consequence that the pair (p, q) has the WMP, but also provides many more natural examples of pairs having a given maximizing property.
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Dates et versions

hal-02974714 , version 1 (22-10-2020)

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Luis García-Lirola, Colin Petitjean. On the Weak Maximizing Properties. Banach Journal of Mathematical Analysis, 2021, ⟨10.1007/s43037-021-00141-x⟩. ⟨hal-02974714⟩
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