The equivalence of various definitions for a properly infinite von Neumann algebra to be approximately finite dimensional

Abstract:

If a properly infinite von Neumann algebra on a separable Hilbert space is approximately finite dimensional with respect to the $\ast$-ultrastrong topology, that is, if any finite number of elements may be approximated $\ast$-ultrastrongly by elements of a finite-dimensional sub $\ast$-algebra, then the algebra may be expressed as the bicommutant of an increasing sequence of factors of type ${{\text {I}}_{{2^n}}}$.