Lipschitz-free spaces over Cantor sets and approximation properties

2023/05/12 by Talimdjioski, Filip · 1 citation
#46B28 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B20

paper · doi:10.48550/arxiv.2305.07591

Abstract

Let K=2^ℕ be the Cantor set, let M be the set of all metrics d on K that give its usual (product) topology, and equip M with the topology of uniform convergence, where the metrics are regarded as functions on K². We prove that the set of metrics d\inM for which the Lipschitz-free space F(K,d) has the metric approximation property is a residual F_σδ set in M, and that the set of metrics d\inM for which F(K,d) fails the approximation property is a dense meager set in M. This answers a question posed by G. Godefroy.

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• Lipschitz-free spaces and Bossard's reduction argument

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