von Neumann Algebra Learning Seminar

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