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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.
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 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)
"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)