
Singular Traces
Theory and Applications
De Gruyter (Publisher)
1st Edition
Published on 12. December 2012
Book
Hardback
XVI, 452 pages
978-3-11-026250-6 (ISBN)
Article exhausted; check for reprint
Description
This book is the first complete study and monograph dedicated to singular traces. The text mathematically formalises the study of traces in a self contained theory of functional analysis. Extensive notes will treat the historical development. The final section will contain the most complete and concise treatment known of the integration half of Connes' quantum calculus. Singular traces are traces on ideals of compact operators that vanish on the subideal of finite rank operators. Singular traces feature in A. Connes' interpretation of noncommutative residues. Particularly the Dixmier trace,which generalises the restricted Adler-Manin-Wodzicki residue of pseudo-differential operators and plays the role of the residue for a new catalogue of 'geometric' spaces, including Connes-Chamseddine standard models, Yang-Mills action for quantum differential forms, fractals, isospectral deformations, foliations and noncommutative index theory. The theory of singular traces has been studied after Connes' application to non-commutative geometry and physics by various authors. Recent work by Nigel Kalton and the authors has advanced the theory of singular traces.Singular traces can be equated to symmetric functionals of symmetricsequence or function spaces, residues of zeta functions and heat kernel asymptotics, and characterised by Lidksii and Fredholm formulas. The traces and formulas used in noncommutative geometry are now completely understood in this theory, with surprising new mathematical and physical consequences. For mathematical readers the text offers fundamental functional analysis results and, due to Nigel Kalton's contribution, a now complete theory of traces on compact operators. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and access to the deeper mathematical features of traces on ideals associated to the harmonic sequence. These features, not known and not discussed in general texts on noncommutative geometry, are undoubtably physical and probe to the fascinating heart of classical limits and quantization.
More details
Series
Language
English
Place of publication
Berlin/Boston
Germany
Target group
Professional and scholarly
US School Grade: College Graduate Student
Illustrations
5 s/w Abbildungen
5 schw.-w. Abb.
Dimensions
Height: 24 cm
Width: 17 cm
Weight
914 gr
ISBN-13
978-3-11-026250-6 (9783110262506)
Schweitzer Classification
Other editions
New editions

Steven Lord | Fedor Sukochev | Dmitriy Zanin
Theory
Book
07/2021
2nd Edition
De Gruyter
€169.95
Shipment within 5-7 days
Persons
Steven Lord, University of Adelaide, Australia; Fedor Sukochev andDmitriy Zanin, University of New South Wales, Sydney, Australia.