Analysis Seminar

Xuanlong Fu, University of Toronto

"Tracial  oscillation zero and stable rank one"

Let A be a separable (not necessarily unital) simple C*-algebra with strict comparison. We show that if A has tracial approximate oscillation zero then A has stable rank one and the canonical map \Gamma from the Cuntz semigroup of A to the corresponding lower-semicontinuous affine function space is surjective. The converse also holds.

As a by-product, we find that a separable simple C*-algebra, which has almost stable rank one must have stable rank one, provided it has strict comparison and the canonical map \Gamma is surjective.

This is a joint work with Huaxin Lin.

This seminar will be held jointly online and in person:

• Zoom link: https://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09
• Room: MC 5501