Satish Pandey, Department of Pure Mathematics, University of Waterloo
“Projections
in
von
Neumann
Algebras
-
Part
II
(continued)”
We’ll begin with a quick review of the material covered before the break and subsequently wrap up our introduction to projections with a few interesting results. We will show that the collection of Murray-von Neumann equivalence classes of projections forms a partially ordered set, and is in fact totally ordered when the algebra in question is a factor. As an application of the double commutant theorem, we will prove that every von Neumann algebra admits a polar decomposition.
MC 5403