Distance between unitary orbits of normal elements in simple $C^*$-algebras of real rank zero -- I

Prof. Shanwen Hu  (East China Normal University)

10:00 am to 11:00 am, Mar 20th, 2014   Science Building A1510

Abstract:

Let $x$ and $y$ be two normal elements in a unital simple $C^*$-algebra $A$. We introduce a function $D_c(x,y)$ and show that in a unital simple AF-algebra, there is a constant $1 > C > 0$ such that $C \cdot D_c(x,y) \le \mbox{dist}(U(x),U(y)) \le D_c(x,y)$, where $U(x)$ and $U(y)$ are the closures of the orbits of $x$ and $y$, respectively. We also generalize this to unital simple $C^*$-algebras wih real rank zero, stable rank one and weakly unperforated $K_0$-group. More complicated estimates are given in the presence of non-trivial $K_1$-information.

This is a joint work with Huaxin Lin.