Singular Traces / [Set Singular Traces, Volume 1+2]

Buch | Hardcover
LXX, 860 Seiten
2023
De Gruyter (Verlag)
978-3-11-070318-4 (ISBN)

Lese- und Medienproben

Singular Traces / [Set Singular Traces, Volume 1+2]
198,95 inkl. MwSt

This book is the second edition of the first complete study and monograph dedicated to singular traces. The first volume 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, updated in this second edition on the fundamental new approach for compact operators, the Pietsch correspondence. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions. An operator based theory of pseudodifferential operators is used to detail the deep association between the noncommutative residue in differential geometry and singular traces. The second 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.

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

"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

Erscheinungsdatum
Reihe/Serie De Gruyter Studies in Mathematics ; 46
Singular Traces
Verlagsort Berlin/Boston
Sprache englisch
Maße 170 x 240 mm
Gewicht 1804 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Schlagworte Diximier Trace • Hilbertraum • pseudo-differential operator • Singular Trace
ISBN-10 3-11-070318-1 / 3110703181
ISBN-13 978-3-11-070318-4 / 9783110703184
Zustand Neuware
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