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Some remarks on the Grothendieck property of spaces of Lipschitz functions

Prof. Christian Bargetz (Universität Innsbruck , Austria) ORCID
Session: Lipschitz-free spaces Talk
Abstract

We discuss a number of conditions for a metric space $M$ which imply that the space of Lipschitz functions $\mathrm{Lip}_0(M)$ admits a continuous operator onto $\ell_1$. Using these results, we provide several conditions for a space M implying that $\mathrm{Lip}_0(M)$ is not a Grothendieck space.

This is joint work with Jerzy Kąkol and Damian Sobota.