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.
General
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