Noncommutative Geometry Seminar

Date: April 1, 2015

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Ken Dykema, Texas A&M University

Title: Perturbation formulas for traces on normed ideals

Abstract: Trace perturbation formulas are expressions for $\tau(f(H_0+V)-f(H_0))$ where $\tau$ is a trace, $H_0$ and $V$ are operators ($H_0$ is often allowed to be unbounded) and $f$ is a function belonging to a suitable class. The classical case, where $\tau$ is the classical trace on $B(\mathcal{H})$ and $V$ is a trace-class operator, was considered by Krein. We prove analogous results, for $\tau$ a trace on an ideal $\mathcal{I}$ of operators, with $V\in\mathcal{I}$. We will also discuss higher order perturbation formulas.