UID:
almafu_9959899575202883
Format:
1 online resource (XXX, 386 p.)
Edition:
2nd corr. and exten. edition
ISBN:
9783110378054
Series Statement:
De Gruyter Studies in Mathematics ; 46/1
Content:
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.
Note:
Frontmatter --
,
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 ℒ1,∞ --
,
Introduction --
,
6 Dixmier traces and positive traces --
,
7 Diagonal formulas for traces --
,
8 Heat trace and ζ-function formulas --
,
9 Criteria for measurability --
,
A Miscellaneous results --
,
Bibliography --
,
Index
,
In English.
Additional Edition:
ISBN 9783110392319
Additional Edition:
ISBN 9783110377798
Language:
English
DOI:
10.1515/9783110378054
URL:
https://doi.org/10.1515/9783110378054
URL:
https://www.degruyter.com/isbn/9783110378054
URL:
https://doi.org/10.1515/9783110378054
URL:
https://www.degruyter.com/isbn/9783110378054
