Amenability, completely bounded projections, dynamical systems and   smooth orbits
  We describe a general method to construct completely bounded idempotent mappings on operator spaces, starting from amenable semigroups of completely bounded mappings. We then explore several applications of that method to injective operator spaces, fixed points of completely contractive mappings, Toeplitz operators, dynamical systems and similarity orbits of group representat ions. 
Daniel Belti\c{t}\u{a} and Bebe Prunaru