# Estimating Dixmier traces of Hankel operators in Lorentz ideals

## TL;DR

This paper investigates Dixmier traces of Hankel operators in Lorentz ideals, extending previous results to powers $p \,\geq\, 1$, providing exact formulas for specific cases, and constructing non-measurable examples.

## Contribution

It generalizes the calculation of Dixmier traces for Hankel operators to broader Lorentz ideals and powers, including explicit formulas for certain cases and new non-measurable examples.

## Key findings

- Exact Dixmier trace formulas for $p=2,4,6$
- Upper and lower bounds for general $p$
- Construction of non-measurable Hankel operators

## Abstract

In this paper we study Dixmier traces of powers of Hankel operators in Lorentz ideals. We extend results of Engli\v{s}-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.