Estimating Dixmier traces of Hankel operators in Lorentz ideals

Journal article, 2020

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≥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.