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Volume 2 Trace Formulas
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Steven Lord
Language:
English
Published/Copyright:
2023
About this book
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.
Author / Editor information
Steven Lord, U of Adelaide, Australia; Fedor Sukochev, Dmitriy Zanin and Edward McDonald, U of New South Wales, Australia.
Topics
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Frontmatter
I -
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Preface
V -
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Notations
VII -
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Contents
XIII -
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Introduction
XVII - Part I: Trace and integral formulas
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1 Bounded operators and pseudodifferential operators
1 -
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2 Trace formulas
129 -
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3 Integration formulas
167 - Part II: The principal symbol mapping in noncommutative geometry
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4 Integration formula for the noncommutative plane
207 -
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5 A C∗-algebraic approach to principal symbols and trace formulas
278 -
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6 Quantum differentiability for the Euclidean plane
349 - Part III: Further applications
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7 Connes character formula
389 -
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8 Density of states
426 -
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Bibliography
457 -
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Index
469
Publishing information
Pages and Images/Illustrations in book
eBook published on:
April 3, 2023
eBook ISBN:
9783110700176
Hardcover published on:
April 3, 2023
Hardcover ISBN:
9783110700008
Edition:
2nd corr. and exten. edition
Pages and Images/Illustrations in book
Front matter:
40
Main content:
474
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
