## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, March 2, 2016 — 2:30 PM EST

**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

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.