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An Introduction to C*-Algebras and the Classification Program: Advanced Courses in Mathematics - CRM Barcelona

Autor Karen R. Strung Editat de Francesc Perera
en Limba Engleză Paperback – 16 dec 2020
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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Specificații

ISBN-13: 9783030474645
ISBN-10: 303047464X
Pagini: 322
Ilustrații: XIII, 322 p.
Dimensiuni: 168 x 240 mm
Greutate: 0.54 kg
Ediția:1st ed. 2021
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Advanced Courses in Mathematics - CRM Barcelona

Locul publicării:Cham, Switzerland

Cuprins

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.

Recenzii

“The book is extremely readable. … The book is also self-contained, and cross-references to results and definitions in the text are clear and precise. … this book is a very welcome contribution to the literature. … On the whole, the book is well written and engaging.” (Elizabeth Anne Gillaspy, Mathematical Reviews, March, 2023)

“The book under review provides an overview of this classification theorem, together with a thorough introduction to the general theory of C*-algebras.” (Zhuang Niu, zbMATH 1479.46003, 2022)

Notă biografică

​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.


Textul de pe ultima copertă

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.

Caracteristici

Includes well-explained examples Gives a comprehensive overview on the theory of C*-algebras Evolves from a course given at the CRM in Barcelona