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https://hdl.handle.net/2440/74697
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Type: | Journal article |
Title: | Traces of compact operators and the noncommutative residue |
Author: | Kalton (late), N. Lord, S. Potapov, D. Sukochev, F. |
Citation: | Advances in Mathematics, 2013; 235:1-55 |
Publisher: | Academic Press Inc Elsevier Science |
Issue Date: | 2013 |
ISSN: | 0001-8708 1090-2082 |
Statement of Responsibility: | Nigel Kalton, Steven Lord, Denis Potapov, Fedor Sukochev |
Abstract: | We extend the noncommutative residue of M.Wodzicki on compactly supported classical pseudo-differential operators of order - d and generalise A. Connes' trace theorem, which states that the residue can be calculated using a singular trace on compact operators. Contrary to the role of the noncommutative residue for the classical pseudo-differential operators, a corollary is that the pseudo-differential operators of order -d do not have a 'unique' trace; pseudo-differential operators can be non-measurable in Connes' sense. Other corollaries are given clarifying the role of Dixmier traces in noncommutative geometry, including the definitive statement of Connes' original theorem. © 2012 Elsevier Ltd. |
Keywords: | Noncommutative residue Connes’ trace theorem Lidskii theorem Noncommutative geometry Spectral theory Singular trace |
Rights: | Copyright © 2012 Elsevier Ltd. All rights reserved. |
DOI: | 10.1016/j.aim.2012.11.007 |
Grant ID: | ARC |
Published version: | http://dx.doi.org/10.1016/j.aim.2012.11.007 |
Appears in Collections: | Aurora harvest 4 Mathematical Sciences publications |
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