We present a new formula to compute Dixmier traces of pseudodifferential operators (respectively, almost periodic pseudodifferential operators) of order −n on n-dimensional compact Riemannian manifolds (respectively, ). Under a natural condition on the operator T, we show that , where G is any bounded neighborhood of and is the Brown spectral measure of T. If T is measurable, then the ω-limit may be replaced with the true (ordinary) limit. Our approach works equally well in both type I and II settings.
Nous présentons une nouvelle formule pour calculer les traces de Dixmier des opérateurs pseudodifférentiels (respectivement, des opérateurs pseudodifférentiels presque périodiques) d'ordre −n sur des variétés compactes de dimension n (respectivement, ). Lorsque T satisfait une condition naturelle, nous montrons que , où G est un voisinage borné de 0 dans et est la mesure spectrale de Brown de T. Si T est mesurable, on peut remplacer la limite faible par la limite au sens usuel. Notre approche s'applique aux types I et II.
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Published online:
Nurulla A. Azamov 1; Fyodor A. Sukochev 1
@article{CRMATH_2005__340_2_107_0, author = {Nurulla A. Azamov and Fyodor A. Sukochev}, title = {A {Lidskii} type formula for {Dixmier} traces}, journal = {Comptes Rendus. Math\'ematique}, pages = {107--112}, publisher = {Elsevier}, volume = {340}, number = {2}, year = {2005}, doi = {10.1016/j.crma.2004.12.005}, language = {en}, }
Nurulla A. Azamov; Fyodor A. Sukochev. A Lidskii type formula for Dixmier traces. Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 107-112. doi : 10.1016/j.crma.2004.12.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.12.005/
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