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Estimating Dixmier traces of Hankel operators in Lorentz ideals

Goffeng, Carl Henrik Tryggve Magnus LU and Usachev, Alexandr (2020) In Journal of Functional Analysis 279(7).
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 ≥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 pand any Lorentz ideal, examples of non-measurable Hankel operators.
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author
and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Hankel operator, Hardy space, Dixmier trace, Besov space
in
Journal of Functional Analysis
volume
279
issue
7
article number
108688
publisher
Elsevier
external identifiers
  • scopus:85087413080
ISSN
0022-1236
DOI
10.1016/j.jfa.2020.108688
language
English
LU publication?
no
id
f0972a0d-8942-4cde-b166-74739bdbe144
date added to LUP
2021-03-12 12:05:32
date last changed
2022-04-19 05:06:59
@article{f0972a0d-8942-4cde-b166-74739bdbe144,
  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 ≥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 pand any Lorentz ideal, examples of non-measurable Hankel operators.}},
  author       = {{Goffeng, Carl Henrik Tryggve Magnus and Usachev, Alexandr}},
  issn         = {{0022-1236}},
  keywords     = {{Hankel operator; Hardy space; Dixmier trace; Besov space}},
  language     = {{eng}},
  number       = {{7}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Functional Analysis}},
  title        = {{Estimating Dixmier traces of Hankel operators in Lorentz ideals}},
  url          = {{http://dx.doi.org/10.1016/j.jfa.2020.108688}},
  doi          = {{10.1016/j.jfa.2020.108688}},
  volume       = {{279}},
  year         = {{2020}},
}