Dixmier traces generated by exponentiation invariant generalised limits

Abstract

We define a new class of singular positive traces on the ideal ${\mathcal{M}}_{1,\infty }$ of $B(H)$ generated by exponentiation invariant generalized limits. We prove that this new class is strictly contained in the class of all Dixmier traces. We also prove a Lidskii-type formula for this class of traces.