Morita Equivalence and Continuous-Trace $C^*$-Algebras (Mathematical Surveys & Monographs) by Iain Raeburn (PDF)

Description

In this text, the authors give a modern treatment of the classification of continuous-trace $C^*$-algebras up to Morita equivalence. This includes a detailed discussion of Morita equivalence of $C^*$-algebras, a review of the necessary sheaf cohomology, and an introduction to recent developments in the area. The book is accessible to students who are beginning research in operator algebras after a standard one-term course in $C^*$-algebras. The authors have included introductions to necessary but nonstandard background. Thus they have developed the general theory of Morita equivalence from the Hilbert module, discussed the spectrum and primitive ideal space of a $C^*$-algebra including many examples, and presented the necessary facts on tensor products of $C^*$-algebras starting from scratch. Motivational material and comments designed to place the theory in a more general context are included. The text is self-contained and would be suitable for an advanced graduate or an independent study course.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book contains nearly all of the important results that one should know in order to start mastering the concept of Morita equivalence of C*-algebras. Williams’ other book, “Crossed Products of C*-Algebras”, refers to this one in many places, which is an indication of its wealth of information. The reader will find that the proofs are clear and that the authors’ writing style makes for easier reading.

⭐This book provides an excellent introduction to Morita Equivalence and Continuous-trace C*-algebras. It is written at a level accesible to graduate students who wish to begin work in these areas. The book is filled with many basic C*-algebra facts which one is hard pressed to find written down in other places, and also gives a nice presentation of Hilbert modules and imprimitivity bimodules. Furthermore the book presents some of the bigger results of the theory, and gives some of the background necessary for these results (sheaf cohomology for instance). Overall, this is one of the best math books I have ever read.

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