Theory
Description
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.
Reviews / Votes
"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
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Content
- Intro
- 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 L ( H)
- Introduction
- 3 Calkin correspondence for norms and traces
- 4 Pietsch correspondence
- 5 Spectrality of traces
- Part III: Formulas for traces on L⊂&1,8&/sub&
- Introduction
- 6 Dixmier traces and positive traces
- 7 Diagonal formulas for traces
- 8 Heat trace and ?-function formulas
- 9 Criteria for measurability
- A Miscellaneous results
- Bibliography
- Index
