Dixmier traces and residues on weak operator ideals
Journal article, 2020

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. (C) 2020 Elsevier Inc. All rights reserved.

Connes' trace theorem

Modulated operators

Singular traces

Pseudo-differential operators


Magnus C H T Goffeng

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

Alexandr Usachev

Central South University

Journal of Mathematical Analysis and Applications

0022-247X (ISSN) 1096-0813 (eISSN)

Vol. 488 2 124045

Subject Categories

Algebra and Logic


Mathematical Analysis



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