  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
$\mathrm C^*$-algebras that arise from suitable families of constraints, which
we call support expansion $\mathrm C^*$-algebras. In the discrete setting,
support expansion $\mathrm C^*$-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 $\mathrm
C^*$-algebras inside $\mathcal B(L^2(\mathbb R))$ is extremely rich, with
uncountable ascending chains, descending chains, and antichains.

Operator Algebras;Functional Analysis