[Set Singular Traces, Volume 1+2] | Buch

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Sprache: Englisch

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Beschreibung

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.

Erscheinungsjahr:	2023
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	LXX 860 S.
ISBN-13:	9783110703184
ISBN-10:	3110703181
Sprache:	Englisch
Hersteller:	De Gruyter
Maße:	58 x 186 x 243 mm
Erscheinungsdatum:	22.05.2023
Gewicht:	1,822 kg

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