Roe-like C*-algebras for actions on meausure spaces

Given a group action on a measure space X, one can generate a C*-algebra by considering bounded operators on L^2(X) that have "finite dynamical propagation". This construction is inspired by the definition of Roe algebras of metric spaces, and was originally motivated by the study of the Roe algebras of certain metric spaces of dynamical origin (warped cones).

Rather than using C*-algebras, one would usually study group actions on measure spaces in terms of von Neumann algebras. It is then an interesting fact that this C*-algebra does carry meaningful information about the dynamical system. For example, it be used to recognise strong ergodicity (this property is a strong negation of Zimmer amenability). This fact can be proved by investigating spectral properties of some Markov operators which are of independent interest.

This talk will be an introduction to this circle of ideas.