Amenable Action and Invariant mean - Kannan, K. (International Journal of Pure and Applied Mathematics, 2014)
We have been thinking also about the possibility of getting a direct proof of Invariant Approximation Property for amenable groups that uses some averaging procedure and does not use von Neumann algebras as in John Roe book. This sounds that like there is a special version of the Invariant Approximation Property (IAP) for von Neumann algebras which is different to the standard one.
Keywords: Amenable; Uniform Roe algebras; Invariant approximation property