Volume 2 Trace Formulas

Steven Lord; Edward McDonald; Fedor Sukochev; Dmitriy Zanin

Published by De Gruyter 2023

Volume 2 Trace Formulas

Steven Lord , Edward McDonald , Fedor Sukochev and Dmitriy Zanin

Part of the multi-volume work Singular Traces

Volume 46/2 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110700176

Overview
Contents

About this book

This volume introduces noncommutative integration theory on semifinite von Neumann algebras and the theory of singular traces for symmetric operator spaces. Deeper aspects of the association between measurability, poles and residues of spectral zeta functions, and asymptotics of heat traces are studied. Applications in Connes’ noncommutative geometry that are detailed include integration of quantum differentials, measures on fractals, and Connes’ character formula concerning the Hochschild class of the Chern character.

Author / Editor information

Steven Lord, U of Adelaide, Australia; Fedor Sukochev, Dmitriy Zanin and Edward McDonald, U of New South Wales, Australia.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Notations Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	XIII
Introduction Publicly Available Download PDF	XVII
Part I: Trace and integral formulas
1 Bounded operators and pseudodifferential operators Requires Authentication Unlicensed Licensed Download PDF	1
2 Trace formulas Requires Authentication Unlicensed Licensed Download PDF	129
3 Integration formulas Requires Authentication Unlicensed Licensed Download PDF	167
Part II: The principal symbol mapping in noncommutative geometry
4 Integration formula for the noncommutative plane Requires Authentication Unlicensed Licensed Download PDF	207
5 A C∗-algebraic approach to principal symbols and trace formulas Requires Authentication Unlicensed Licensed Download PDF	278
6 Quantum differentiability for the Euclidean plane Requires Authentication Unlicensed Licensed Download PDF	349
Part III: Further applications
7 Connes character formula Requires Authentication Unlicensed Licensed Download PDF	389
8 Density of states Requires Authentication Unlicensed Licensed Download PDF	426
Bibliography Requires Authentication Unlicensed Licensed Download PDF	457
Index Requires Authentication Unlicensed Licensed Download PDF	469

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 2nd corr. and exten. edition
Pages
- Front matter: 40
- Main content: 474
Keywords: Diximier Trace; Hilbert Space; Singular Trace; Pseudo Differential Operator

eBook

Published: April 3, 2023
ISBN: 9783110700176

Hardcover

Published: April 3, 2023
ISBN: 9783110700008