Abstract:
We describe analogs of AF C*-algebras which act on L^p spaces. For the ``good'' ones (which we call spatial), there is an analog of the Elliott classification theorem in the C* case. The spatial L^p AF algebras also have good properties. The development requires consideration of direct limit of L^p operator algebras and unitization of L^p operator algebras.
This is joint work with Maria Grazia Viola.