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Bruno de Mendonça Braga

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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

Dynamical $\mathrm C^*$-algebras and coarse geometry

Both the uniform Roe algebras and the quasi-local algebras encode the large scale geometry of metric spaces. Whether these algebras coincide is a question which goes back to Roe and has only been recently solved by Ozawa. We propose a dynamical point of view on this problem. Given a set $X$, every map $h\colon X\to\mat...

Bruno de Mendonça Braga · 0 citations