Dixmier traces and residues on weak operator ideals
(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:
https://lup.lub.lu.se/record/504c6d5a-3bc6-4ce5-9a81-bb996dd629c2
- author
- Goffeng, Carl Henrik Tryggve Magnus LU and Usachev, Alexandr
- publishing date
- 2020
- 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}}, }