On the Weak Maximizing Properties

2020/07/03 by Garcia-Lirola, Luis C., Petitjean, Colin
#46B20 (Primary) 46B04 #54E50 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2007.01939

Abstract

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 (ℓ_p,ℓ_q) has the WMP, but also provides many more natural examples of pairs having a given maximizing property.

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