Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states
The von Neumann algebra free product of arbitary finite dimensional von Neumann algebras with respect to arbitrary faithful states, at least one of which is not a trace, is found to be a type~III factor possibly direct sum a finite dimensional algebra. The free product state on the type~III factor is what we call an extremal almost periodic state, and has centralizer isomorphic to $L(\freeF_\infty)$. This allows further classification the type~III factor and provides another construction of full type~III$_1$ factors having arbitrary $\Sd$~invariant of Connes. The free products considered in this paper are not limited to free products of finite dimensional algebras, but can be of a quite general form.
- Pub Date:
- January 1996
- Mathematics - Functional Analysis;
- Mathematics - Operator Algebras
- 46 pages. To appear in a volume of Fields Institute Communications edited by D.V. Voiculescu. This .tex file uses a .sty file for this communitation series, (fic.sty), which together with supporting files is included in this 'tar'ed directory. Documentation for these can be obtained from the American Mathematical Society by ftp from e-math.ams.org or on WWW at ftp://e-math.ams.org/pub/author-info/packages/fic/amstex/