2022/02/14 by Kadets, Vladimir, Roldán, Óscar
#46B04 (Primary) 46B20 #46B87 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2202.06855
Given a pointed metric space M, we study when there exist n-dimensional linear subspaces of Lip0(M) consisting of strongly norm-attaining Lipschitz functionals, for n∈ℕ. We show that this is always the case for infinite metric spaces, providing a definitive answer to the question. We also study the possible sizes of such infinite-dimensional closed linear subspaces Y, as well as the inverse question, that is, the possible sizes of the metric space M given that such a subspace Y exists. We also show that if the metric space M is σ-precompact, then the aforementioned subspaces Y need to be always separable and isomorphically polyhedral, and we show that for spaces containing [0,1] isometrically, they can be infinite-dimensional.