Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results

Abstract

In this paper we establish uniqueness theorems for the noncommutative residue and the canonical trace on pseudodifferential operators on noncommutative tori of arbitrary dimension. The former is the unique trace up to constant multiple on integer order pseudodifferential operators.The latter is the unique trace up to constant multiple on non-integer order pseudodifferential operators. This improves previous uniqueness results by Fathizadeh-Khalkhali, Fathizadeh-Wong, and Lévy-Neira-Paycha.

References in corpus (2)

• The Gauss-Bonnet Theorem for the noncommutative two torus
• Hypergeometric function and Modular Curvature II. Connes-Moscovici functional relation after Lesch's work

Cited by in corpus (5)

• Spectral Metric and Einstein Functionals
• Semiclassical Weyl law and exact spectral asymptotics in noncommutative geometry
• Connes Trace Theorem for Curved Noncommutative Tori. Application to Scalar Curvature
• Dixmier Trace Formulas and Negative Eigenvalues of Schroedinger Operators on Curved Noncommutative Tori
• Pseudodifferential Operators on Noncommutative Tori: a Survey