<p><p>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.</p></p>

[Set Singular Traces, Volume 1+2] (De Gruyter Studies in Mathematics, 46)

Science & Math

Steven Lord

Sukochev, Fedor

Zanin, Dmitriy

Mathematics

de Gruyter

The Tigers' Second Quest: Tigers' Quest II

Literature & Fiction

Independently published

After The Quest: Tigers Quest III

Children's Books

Animals

See the best price to sell, buy, or rent books by Steven Lord. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Steven Lord