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Dixmier traces and residues on weak operator ideals

Goffeng, Carl Henrik Tryggve Magnus LU and Usachev, Alexandr (2020) In Journal of Mathematical Analysis and Applications 488(2).
Abstract
We develop the theory of modulated operators in general principal ideals of compact operators. For Laplacian modulated operators we establish Connes' trace formula in its local Euclidean model and a global version thereof. It expresses Dixmier traces in terms of the vector-valued Wodzicki residue. We demonstrate the applicability of our main results in the context of log-classical pseudo-differential operators, studied by Lesch, and a class of operators naturally appearing in noncommutative geometry.
Please use this url to cite or link to this publication:
author
and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Singular traces, Modulated operators, Pseudo-differential operators, Connes' trace theorem
in
Journal of Mathematical Analysis and Applications
volume
488
issue
2
article number
124045
publisher
Elsevier
external identifiers
  • scopus:85082691361
ISSN
0022-247X
DOI
10.1016/j.jmaa.2020.124045
language
English
LU publication?
no
id
504c6d5a-3bc6-4ce5-9a81-bb996dd629c2
date added to LUP
2021-03-12 12:03:59
date last changed
2022-04-19 05:06:59
@article{504c6d5a-3bc6-4ce5-9a81-bb996dd629c2,
  abstract     = {{We develop the theory of modulated operators in general principal ideals of compact operators. For Laplacian modulated operators we establish Connes' trace formula in its local Euclidean model and a global version thereof. It expresses Dixmier traces in terms of the vector-valued Wodzicki residue. We demonstrate the applicability of our main results in the context of log-classical pseudo-differential operators, studied by Lesch, and a class of operators naturally appearing in noncommutative geometry.}},
  author       = {{Goffeng, Carl Henrik Tryggve Magnus and Usachev, Alexandr}},
  issn         = {{0022-247X}},
  keywords     = {{Singular traces; Modulated operators; Pseudo-differential operators; Connes' trace theorem}},
  language     = {{eng}},
  number       = {{2}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Mathematical Analysis and Applications}},
  title        = {{Dixmier traces and residues on weak operator ideals}},
  url          = {{http://dx.doi.org/10.1016/j.jmaa.2020.124045}},
  doi          = {{10.1016/j.jmaa.2020.124045}},
  volume       = {{488}},
  year         = {{2020}},
}