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Creators/Authors contains: "Braga, Bruno M."

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  1. ; ; (, Pacific Journal of Mathematics)
    We propose a quantization of coarse spaces and uniform Roe algebras. The objects are based on the quantum relations introduced by N. Weaver and require the choice of a represented von Neumann algebra. In the case of the diagonal inclusion ell_infty(X) subset B(ell_2(X)), they reduce to the usual constructions. Quantum metric spaces furnish natural examples parallel to the classical setting, but we provide other examples that are not inspired by metric considerations, including the new class of support expansion C*-algebras. We also work out the basic theory for maps between quantum coarse spaces and their consequences for quantum uniform Roe algebras. 
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    Free, publicly-accessible full text available January 1, 2026
  2. ; (, Comptes Rendus. Mathématique)
    We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be ℝ -linear. We obtain a generalization of the aforementioned result to completely coarse maps defined on the unit ball of an operator space. By relaxing the condition to a small scale one, we prove that there are many non-linear examples of maps which are completely Lipschitz in small scale. We define a geometric parameter for homogeneous Hilbertian operator spaces which imposes restrictions on the existence of such maps. 
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    Free, publicly-accessible full text available December 3, 2025
  3. ; ; ; ; (, Mathematische Zeitschrift)
    We provide a characterization of when a coarse equivalence between coarse disjoint unions of expander graphs is close to a bijective coarse equivalence. We use this to show that if the uniform Roe algebras over metric spaces that are coarse unions of expanders graphs are isomorphic, then the metric spaces must be bijectively coarsely equivalent. 
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  4. ; ; (, Mathematische Annalen)
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  5. ; ; ; ; (, Journal of Functional Analysis)
    We study which von Neumann algebras can be embedded into uniform Roe algebras and quasi-local algebras associated with a uniformly locally finite metric space X. Under weak assumptions, these C*-algebras contain embedded copies of certain matrix algebras. We aim to show they cannot contain any other von Neumann algebras. One of our main results shows that the only embedded von Neumann algebras are the “obvious” ones. 
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  6. ; (, Mathematische Zeitschrift)
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  7. ; ; ; ; ; (, Inventiones mathematicae)
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  8. ; (, Proceedings of the American Mathematical Society)
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