An introduction to C*-algebras and the classification program / Karen R. Strung.
Strung, Karen R.; Perera, Francesc, 1970- editor.
2021
QA326
Available Online

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Title
An introduction to C*-algebras and the classification program / Karen R. Strung.
Author
Strung, Karen R.
ISBN
9783030474652 (electronic bk.)
3030474658 (electronic bk.)
9783030474645 (print)
303047464X
DOI
https://doi.org/10.1007/978-3-030-47465-2
Publication Details
Cham : Birkhäuser, 2021.
Language
English
Description
1 online resource (333 pages)
Item Number
10.1007/978-3-030-47465-2 doi
Call Number
QA326
Dewey Decimal Classification
512/.55
Summary
This book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed February 18, 2021).
Added Author
Perera, Francesc, 1970- editor.
Series
Advanced courses in mathematics, CRM Barcelona.
Available in Other Form
An Introduction to C*-Algebras and the Classification Program.
Linked Resources
Online Access
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All Resources
Banach algebras and spectral theory
The Gelfand representation
C*-algebra basics
Positive elements
Positive linear functionals and representations
Weak and strong operator topologies and von Neumann algebras
Tensor products for C*-algebras
Completely positive maps
Inductive limits and approximately finite (AF) C*-algebras
Group C*-algebras and crossed products
Cuntz algebras
Quasidiagonal C*-algebras
K-theory for unital C*-algebras
Classification of AF-algebras
Nuclear dimension
Strongly self-absorbing algebras
The Jiang-Su algebra
Strict comparison and the Cuntz semigroup
The Classification Theorem and the Toms-Winter Theorem.

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