Completely Contractive Projections on Preduals of Injective von Neumann Algebras
by
Ping Wong Ng
University of California at Los Angeles
Coauthors: Edward Effros

Our goal is to use operator space techniques to study the local geometry of von Neumann algebra preduals. A basic step in such a program would be to prove the following result (which we have done):

Let R be an injective von Neumann algebra. Let V be a finite dimensional subspace of R_* (the predual of R). Then V is completely isometric to a noncommutative l¹ space iff V is the range of a completely contractive projection on R_*.

It turns out that viewing R_* as an operator space (as opposed to a Banach space) leads to certain interesting simplifications.

Date received: April 30, 1999