Journal of Operator Theory

Volume 92, Issue 2, Autumn 2024 pp. 463-504.

Support expansion $C^*$-algebras

Authors: B.M. Braga (1), J. Eisner (2), and D. Sherman (3)
Author institution: (1) Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil
(2) University of Virginia, $141$ Cabell Drive, Kerchof Hall, P.O. Box 400137, Charlottesville, VA 22904-4137, U.S.A.
(3) University of Virginia, $141$ Cabell Drive, Kerchof Hall, P.O. Box 400137, Charlottesville, VA 22904-4137, U.S.A

Summary: We consider operators on $L^2$-spaces that expand the support of vectors in a manner controlled by some constraint function. The primary objects of study are $C^*$-algebras that arise from suitable families of constraints, which we call support expansion $C^*$-algebras. In the discrete setting, support expansion $C^*$-algebras are classical uniform Roe algebras, and the continuous version featured here provides examples of ``measurable'' or ``quantum'' uniform Roe algebras as developed in a companion paper. We find that in contrast to the discrete setting, the poset of support expansion $C^*$-algebras inside $\mathcal{B}(L^2(\mathbb{R}))$ is extremely rich, with uncountable ascending chains, descending chains, and antichains.

DOI: http://dx.doi.org/10.7900/jot.2022nov07.2412
Keywords: support expansion, uniform Roe algebras

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