Finite dimensional approximations and coactions for operator algebras
Adam Dor-On (University of Illinois at Urbana-Champaign)
Thursday 4th February 16:00-17:00 Contact the organizers for Zoom coordinates
Finite dimensional approximations for all representations of a C*-algebra are available whenever some injective representation has such an approximation. This is a classical result of Exel and Loring from 1992. We extend this paradigm to general (possibly non-self-adjoint) operator algebras.
Our work is intimately related to the question, studied by Clouatre and Ramsey, of whether the maximal C*-cover of an operator algebra is residually-finite dimensional when the algebra itself is. We resolve this question for semigroup operator algebras as well as various algebras of functions, providing many previously-unattainable examples. A novel key tool in our analysis is the notion of an RFD coaction by a semigroup, whose development uses and extends ideas from the theory of semigroup C*-algebras.