Dixmier traces and residues on weak operator ideals

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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.
Original languageEnglish
Article number124045
JournalJournal of Mathematical Analysis and Applications
Volume488
Issue number2
DOIs
Publication statusPublished - 2020
Externally publishedYes

Subject classification (UKÄ)

  • Mathematical Analysis

Keywords

  • Singular traces
  • Modulated operators
  • Pseudo-differential operators
  • Connes' trace theorem

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