Author

C. Gartland

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Preprint Oct 2026

On the $L$-embeddability of Lipschitz-free spaces in their biduals

A Banach space $X$ is $L$-embedded in its bidual if there is a projection $P\colon X^{**}\to X$ such that $\|x\|=\|Px\|+\|x-Px\|$ for all $x\in X^{**}$. We show that, as long as $X$ has dimension at least $2$, its Lipschitz-free space, denoted by $\mathcal{F}(X)$, is not $L$-embedded in its bidual. Our methods have app...

Bruno de Mendonça Braga, C. Gartland, G. Lancien et al. · 2 citations · ⚡1

Preprint Sep 2026

Uniformly Lipschitz Hyperbolic Group Actions on $\ell^p$

Let $\Gamma$ be a finitely generated hyperbolic group, and let $Q$ denote the conformal dimension of its Gromov boundary $\partial\Gamma$. We prove that for every $p<\frac{Q}{Q-1}$, the group $\Gamma$ admits a proper uniformly Lipschitz affine action on $\ell^p$ with compression exponent $1/p$. The $\ell^p$-space hosti...

C. Gartland, Tian-Yi Zheng · 0 citations