Dixmier traces and residues on weak operator ideals

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Dixmier traces and residues on weak operator ideals. / Goffeng, Carl Henrik Tryggve Magnus; Usachev, Alexandr.

I: Journal of Mathematical Analysis and Applications, Vol. 488, Nr. 2, 124045, 2020.

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

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TY - JOUR

T1 - Dixmier traces and residues on weak operator ideals

AU - Goffeng, Carl Henrik Tryggve Magnus

AU - Usachev, Alexandr

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Singular traces

KW - Modulated operators

KW - Pseudo-differential operators

KW - Connes' trace theorem

UR - http://arxiv.org/abs/1710.08260

U2 - 10.1016/j.jmaa.2020.124045

DO - 10.1016/j.jmaa.2020.124045

M3 - Article

VL - 488

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

M1 - 124045

ER -