Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo
“Kaplansky’s Density Theorem”
Last week we learned that a von Neumann algebra A is a C∗-algebra acting on a Hilbert space H in such a way that the result is WOT-closed. This week we’ll show that if A is a von Neumann algebra of operators on H, but also acts on some other Hilbert space H′, then it’s still WOT-closed as an algebra of operators in B (H′). To do this we will use the Kaplansky Density Theorem, which is a fundamental fact in the theory of von Neumann algebras.
MC 5417