Estimating Dixmier traces of Hankel operators in Lorentz ideals

Abstract

In this paper we study Dixmier traces of powers of Hankel operators in Lorentz ideals. We extend results of Engliš-Zhang to the case of powers $p\ge 1$ and general Lorentz ideals starting from abstract extrapolation results of Gayral-Sukochev. In the special case $p=2,4,6$ we give an exact formula for the Dixmier trace. For general $p$, we give upper and lower bounds on the Dixmier trace. We also construct, for any $p$ and any Lorentz ideal, examples of non-measurable Hankel operators.

22 pages