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.

Readership

Graduate students, research mathematicians, and mathematical physicists working in operator algebras, Morita equivalence, or continuous-trace $C^*$-algebras.