Support expansion $\mathrm C^*$-algebras
Bruno de Mendon\c{c}a Braga, Joseph Eisner, David Sherman

TL;DR
This paper introduces support expansion $ ext{C}^*$-algebras, a class of operator algebras on $L^2$ spaces that generalize uniform Roe algebras to continuous and quantum settings, revealing a rich and complex structure.
Contribution
It defines support expansion $ ext{C}^*$-algebras in continuous and quantum contexts and analyzes their intricate poset structure, extending classical discrete results.
Findings
Support expansion $ ext{C}^*$-algebras generalize uniform Roe algebras.
The poset of these algebras in $L^2( eal)$ is extremely rich.
Uncountable chains and antichains exist within this poset.
Abstract
We consider operators on spaces that expand the support of vectors in a manner controlled by some constraint function. The primary objects of study are -algebras that arise from suitable families of constraints, which we call support expansion -algebras. In the discrete setting, support expansion -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 -algebras inside is extremely rich, with uncountable ascending chains, descending chains, and antichains.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Advanced Topics in Algebra
