Estimating Dixmier traces of Hankel operators in Lorentz ideals

Artikel i vetenskaplig tidskrift, 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.