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(s): Steven Lord, Fedor Sukochev, Dmitriy Zanin
Series: De Gruyter Studies in Mathematics, 46/1
Edition: 2
Publisher: De Gruyter
Year: 2021
Language: English
Pages: 430
Tags: Functional Analysis
Preface
Notations
Contents
Introduction
Part I: Preliminary material
1 What is a singular trace?
2 Singular values and submajorization
Part II: Theory of traces on ideals of β ( H)
Introduction
3 Calkin correspondence for norms and traces
4 Pietsch correspondence
5 Spectrality of traces
Part III: Formulas for traces on β1,β
Introduction
6 Dixmier traces and positive traces
7 Diagonal formulas for traces
8 Heat trace and ΞΆ-function formulas
9 Criteria for measurability
A Miscellaneous results
Bibliography
Index
