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An Introduction to C*-Algebras and the Classification Program

E-BookPDF1 - PDF WatermarkE-Book
322 Seiten
Englisch
Springer International Publishingerschienen am15.12.20201st ed. 2021
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.
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Verfügbare Formate
BuchKartoniert, Paperback
EUR27,81
E-BookPDF1 - PDF WatermarkE-Book
EUR26,74

Produkt

KlappentextThis 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.
Details
Weitere ISBN/GTIN9783030474652
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
FormatE107
Erscheinungsjahr2020
Erscheinungsdatum15.12.2020
Auflage1st ed. 2021
Seiten322 Seiten
SpracheEnglisch
IllustrationenXIII, 322 p.
Artikel-Nr.5852111
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr

Autor

¿Karen R. Strung is a researcher in the Department of Abstract Analysis at the Institute of Mathematics of the Czech Academy of Sciences, in Prague, Czechia. I study the classification and structure of C*-algebras and their connections to dynamical systems.