Trace Formulas: 46 (De Gruyter Studies in Mathematics, 46/2) - Hardcover

Steven Lord; Fedor Sukochev; Dmitriy Zanin; Edward McDonald

 
9783110700008: Trace Formulas: 46 (De Gruyter Studies in Mathematics, 46/2)
Hardcover
ISBN 10: 311070000X ISBN 13: 9783110700008
Publisher: De Gruyter, 2023

Synopsis

This 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.

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About the Author

Steven Lord, U of Adelaide, Australia; Fedor Sukochev, Dmitriy Zanin and Edward McDonald, U of New South Wales, Australia.

From the Back Cover

This volume introduces trace formulas for singular traces on a separable Hilbert space. In general terms, trace formulas compute the value of a singular trace by integration over the principal part of the symbol of a bounded operator. Formulas and symbols are described from several applications in Alain Connes' noncommutative geometry. Singular traces are shown to compute the noncommutative residue in differential geometry using the principal symbol of a pseudodifferential operator. An extension of the symbol map and computation of the noncommutative residue using a trace formula are shown for the noncommutative torus, noncommutative Euclidean space, and the C*-algebra of SU(2)-valued continuous functions. Several other trace formulas from noncommutative geometry are computed using the same principle, including integration of functions over quantum densities, Connes' character formula concerning the Hochschild cohomology class of the Chern character, and extension of the density of states measure in solid state physics.

"About this title" may belong to another edition of this title.

Publisher
De Gruyter
Publication date
2023
Language
English
ISBN 10 
311070000X
ISBN 13 
9783110700008
Binding
Hardcover
Edition number
2
Number of pages
474