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Morita Equivalence and Continuous-Trace $$C^*$$-Algebras
Iain Raeburn, University of Newcastle, NSW, Australia, and Dana P. Williams, Dartmouth College, Hanover, NH
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Mathematical Surveys and Monographs
1998; 327 pp; hardcover
Volume: 60
ISBN-10: 0-8218-0860-5
ISBN-13: 978-0-8218-0860-3
List Price: US$79 Member Price: US$63.20
Order Code: SURV/60

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.

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

Reviews

"The exposition is stimulating and well written, and should be regarded as essential reading for any research student in $$C^*$$-algebras. Indeed, the book has a strong claim to be on the shelves of anybody, student or veteran, working in the subject."

-- Bulletin of the London Mathematical Society

"A beautiful book ... The book provides a very nice introduction to some recent research work of the authors (and others) on the interplay between the theory of group actions on continuous-trace $$C^*$$-algebras and algebraic topology."

-- Zentralblatt MATH

"An extremely useful reader's guide is provided in the introduction that summarizes in a clear and precise way what is in each of the seven chapters and four appendices. The authors have indeed made a serious effort to make this volume self-contained and to keep the required background to a minimum. The writing is clear and details are provided throughout. Although this is a volume that will demand the reader's attention to master the material, there is an air of informality to the writing that makes the reading pleasant and enjoyable. The authors are to be commended for writing a beautiful book that will open the way to researchers wishing to learn about a fascinating area of mathematics."

-- Mathematical Reviews Featured Review

• The algebra of compact operators
• Hilbert $$C^*$$-modules
• Morita equivalence
• Sheaves, cohomology, and bundles
• Continuous-trace $$C^*$$-algebras
• Applications
• Epilogue: The Brauer group and group actions
• The spectrum
• Tensor products of $$C^*$$-algebras
• The imprimitivity theorem
• Miscellany
• Index
• Bibliography