Volume 1 Theory:

Steven Lord; Fedor Sukochev; Dmitriy Zanin

Published by De Gruyter 2021

Volume 1 Theory

Steven Lord , Fedor Sukochev and Dmitriy Zanin

Part of the multi-volume work Singular Traces

Volume 46/1 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110378054

Overview
Contents

About this book

This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes’ noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.

Author information

Steven Lord, University of Adelaide, Australia; Fedor Sukochev and Dmitriy Zanin, University of New South Wales, Sydney, Australia.

Reviews

"Each chapter begins with a summary of the main results and ends with comments and historical notes, which makes the reading pleasant despite the sometimes heavy technical details." Mathematical Reviews

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Notations Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	XI
Introduction Publicly Available Download PDF	XV
Part I: Preliminary material
1 What is a singular trace? Requires Authentication Unlicensed Licensed Download PDF	1
2 Singular values and submajorization Requires Authentication Unlicensed Licensed Download PDF	29
Part II: Theory of traces on ideals of ℒ ( H)
Introduction Requires Authentication Unlicensed Licensed Download PDF	79
3 Calkin correspondence for norms and traces Requires Authentication Unlicensed Licensed Download PDF	83
4 Pietsch correspondence Requires Authentication Unlicensed Licensed Download PDF	113
5 Spectrality of traces Requires Authentication Unlicensed Licensed Download PDF	141
Part III: Formulas for traces on ℒ_1,∞
Introduction Requires Authentication Unlicensed Licensed Download PDF	181
6 Dixmier traces and positive traces Requires Authentication Unlicensed Licensed Download PDF	185
7 Diagonal formulas for traces Requires Authentication Unlicensed Licensed Download PDF	225
8 Heat trace and ζ-function formulas Requires Authentication Unlicensed Licensed Download PDF	249
9 Criteria for measurability Requires Authentication Unlicensed Licensed Download PDF	295
A Miscellaneous results Requires Authentication Unlicensed Licensed Download PDF	355
Bibliography Requires Authentication Unlicensed Licensed Download PDF	367
Index Requires Authentication Unlicensed Licensed Download PDF	381

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 2nd corr. and exten. edition
Audience: Graduate Students, Lecturers, and Researchers in Mathematics and Mathematical Physics; Academic Libraries
Pages
- Front matter: 30
- Main content: 386
Keywords: Singular Trace; Diximier Trace; Pseudo-Differential Operator; Hilbertraum

eBook

Published: July 19, 2021
ISBN: 9783110378054

Hardcover

Published: July 19, 2021
ISBN: 9783110377798