# C*-Algebras and Their Automorphism Groups

### A volume in Pure and Applied Mathematics

Book • Second Edition2018

Edited by:

Søren Eilers and Dorte Olesen

# C*-Algebras and Their Automorphism Groups

### A volume in Pure and Applied Mathematics

Book • Second Edition2018

Edited by:

Søren Eilers and Dorte Olesen

## Book description

This elegantly edited landmark edition of Gert Kjærgård Pedersen’s C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect th ... read full description

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#### Editors' Preface

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#### Chapter 1 - Abstract ${C}^{⁎}$-Algebras

Pages 1-25

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#### Chapter 2 - Concrete ${C}^{⁎}$-Algebras

Pages 27-51

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#### Chapter 3 - Functionals and Representations

Pages 53-119

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#### Chapter 4 - Decomposition Theory

Pages 121-191

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#### Chapter 5 - Weights and Traces

Pages 193-242

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#### Chapter 6 - Type I ${C}^{⁎}$-Algebras

Pages 243-290

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#### Chapter 7 - Automorphism Groups

Pages 291-380

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#### Chapter 8 - Spectral Theory for Automorphism Groups

Pages 381-493

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#### Appendix A

Pages 495-497

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#### References

Pages 499-513

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#### Index

Pages 515-520

### Description

This elegantly edited landmark edition of Gert Kjærgård Pedersen’s C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect the wealth of relevant novel results revealed over the past forty years. Revered from publication for its writing clarity and extremely elegant presentation of a vast space within operator algebras, Pedersen’s monograph is notable for reviewing partially ordered vector spaces and group automorphisms in unusual detail, and by strict intention releasing the C*-algebras from the yoke of representations as Hilbert space operators. Under the editorship of Søren Eilers and Dorte Olesen, the second edition modernizes Pedersen’s work for a new generation of C*-algebraists, with voluminous new commentary, all-new indexes, annotation and terminology annexes, and a surfeit of new discussion of applications and of the author’s later work.

This elegantly edited landmark edition of Gert Kjærgård Pedersen’s C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect the wealth of relevant novel results revealed over the past forty years. Revered from publication for its writing clarity and extremely elegant presentation of a vast space within operator algebras, Pedersen’s monograph is notable for reviewing partially ordered vector spaces and group automorphisms in unusual detail, and by strict intention releasing the C*-algebras from the yoke of representations as Hilbert space operators. Under the editorship of Søren Eilers and Dorte Olesen, the second edition modernizes Pedersen’s work for a new generation of C*-algebraists, with voluminous new commentary, all-new indexes, annotation and terminology annexes, and a surfeit of new discussion of applications and of the author’s later work.

### Key Features

• Covers basic C*-algebras theory in a short and appealingly elegant way, with a few additions and corrections given to the editors by the original author
• Expands coverage to select contemporary accomplishments in C*-algebras of direct relevance to the scope of the first edition, including aspects of K-theory and set theory
• Identifies key modern literature in an updated bibliography with over 100 new entries, and greatly enhances indexing throughout
• Modernizes coverage of algebraic problems in relation to the theory of unitary representations of locally compact groups
• Reviews mathematical accomplishments of Gert K. Pedersen in comments and a biography
• Covers basic C*-algebras theory in a short and appealingly elegant way, with a few additions and corrections given to the editors by the original author
• Expands coverage to select contemporary accomplishments in C*-algebras of direct relevance to the scope of the first edition, including aspects of K-theory and set theory
• Identifies key modern literature in an updated bibliography with over 100 new entries, and greatly enhances indexing throughout
• Modernizes coverage of algebraic problems in relation to the theory of unitary representations of locally compact groups
• Reviews mathematical accomplishments of Gert K. Pedersen in comments and a biography

## Details

### ISBN

978-0-12-814122-9

English

2018

### DOI

https://doi.org/10.1016/C2016-0-03431-9

## Authors

### Gert K. Pedersen

Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

## Editors

### Søren Eilers

Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

### Dorte Olesen

Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark