UID:
almafu_9961035336602883
Format:
1 online resource (XL, 474 p.)
Edition:
2nd corr. and exten. edition
ISBN:
9783110700176
Series Statement:
De Gruyter Studies in Mathematics , 46/2
Content:
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.
Note:
Frontmatter --
,
Preface --
,
Notations --
,
Contents --
,
Introduction --
,
Part I: Trace and integral formulas --
,
1 Bounded operators and pseudodifferential operators --
,
2 Trace formulas --
,
3 Integration formulas --
,
Part II: The principal symbol mapping in noncommutative geometry --
,
4 Integration formula for the noncommutative plane --
,
5 A C∗-algebraic approach to principal symbols and trace formulas --
,
6 Quantum differentiability for the Euclidean plane --
,
Part III: Further applications --
,
7 Connes character formula --
,
8 Density of states --
,
Bibliography --
,
Index
,
Issued also in print.
,
In English.
Additional Edition:
ISBN 9783110700244
Additional Edition:
ISBN 9783110700008
Language:
English
DOI:
10.1515/9783110700176
URL:
https://doi.org/10.1515/9783110700176
URL:
https://www.degruyter.com/isbn/9783110700176
URL:
https://doi.org/10.1515/9783110700176
URL:
https://www.degruyter.com/isbn/9783110700176
