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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.
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.
¿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.
Includes well-explained examples
Gives a comprehensive overview on the theory of C*-algebras
Evolves from a course given at the CRM in Barcelona
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.
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
xiii
322 S. |
| ISBN-13: | 9783030474645 |
| ISBN-10: | 303047464X |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Strung, Karen R. |
| Redaktion: | Perera, Francesc |
| Herausgeber: | Francesc Perera |
| Auflage: | 1st edition 2021 |
| Hersteller: | Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com |
| Maße: | 240 x 168 x 19 mm |
| Von/Mit: | Karen R. Strung |
| Erscheinungsdatum: | 16.12.2020 |
| Gewicht: | 0,565 kg |
¿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.
Includes well-explained examples
Gives a comprehensive overview on the theory of C*-algebras
Evolves from a course given at the CRM in Barcelona
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.
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
xiii
322 S. |
| ISBN-13: | 9783030474645 |
| ISBN-10: | 303047464X |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Strung, Karen R. |
| Redaktion: | Perera, Francesc |
| Herausgeber: | Francesc Perera |
| Auflage: | 1st edition 2021 |
| Hersteller: | Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com |
| Maße: | 240 x 168 x 19 mm |
| Von/Mit: | Karen R. Strung |
| Erscheinungsdatum: | 16.12.2020 |
| Gewicht: | 0,565 kg |
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