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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 $p\geq 1$ 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.'
address: ' Email: goffeng@chalmers.se, usachev@chalmers.seDepartment of Mathematical Sciences Chalmers University of Technology and University of Gothenburg SE-412 96 Gothenburg Sweden'
author:
- 'Magnus Goffeng, Alexandr Usachev'
title: Estimating Dixmier traces of Hankel operators in Lorentz ideals
---

Introduction
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The construction of Dixmier traces goes back to work of Dixmier [@Dixie] who was motivated by the problem of finding a non-normal trace on the von Neumann algebra of bounded operators. Since then Dixmier traces have taken a prominent role in Connes’ program for noncommutative geometry [@C_book] and found applications in the analysis of rough structures such as Julia sets [@juliaconnes], limit sets of quasi-Fuchsian groups [@quasiconnes] and in complex geometry [@EZe; @GG0; @GG]. The non-normality of the Dixmier 