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Fundamentals of the Theory of Operator Algebras. Volume II: Advanced Theory

John R. Ringrose University of Newcastle, Newcastle upon Tyne, England
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Hardcover ISBN: 978-0-8218-0820-7
Product Code: GSM/16
List Price: $95.00 MAA Member Price:$85.50
AMS Member Price: $76.00 Electronic ISBN: 978-1-4704-2073-4 Product Code: GSM/16.E List Price:$89.00
MAA Member Price: $80.10 AMS Member Price:$71.20
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AMS Member Price: $114.00 Click above image for expanded view Fundamentals of the Theory of Operator Algebras. Volume II: Advanced Theory Richard V. Kadison University of Pennsylvania, Philadelphia, PA John R. Ringrose University of Newcastle, Newcastle upon Tyne, England Available Formats:  Hardcover ISBN: 978-0-8218-0820-7 Product Code: GSM/16  List Price:$95.00 MAA Member Price: $85.50 AMS Member Price:$76.00
 Electronic ISBN: 978-1-4704-2073-4 Product Code: GSM/16.E
 List Price: $89.00 MAA Member Price:$80.10 AMS Member Price: $71.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$142.50 MAA Member Price: $128.25 AMS Member Price:$114.00
• Book Details

Volume: 161997; 676 pp
MSC: Primary 46; Secondary 47;

This work and Fundamentals of the Theory of Operator Algebras. Volume I, Elementary Theory present an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology. The book presents the possibility for the design of numerous courses aimed at different audiences.

Praise for both volumes …

“ …these two volumes represent a magnificent achievement. They will be an essential item on every operator algebraist's bookshelves and will surely become the primary source of instruction for research students in von Neumann algebra theory.”

Bulletin of the London Mathematical Society

“Volumes I and II were published in 1982 and 1983. Since then they have quickly established themselves as The Textbooks in operator algebra theory.”

Bulletin of the American Mathematical Society

“One of the splendid features of the original two volumes is their large supply of exercises … which illustrate the results of the text and expand its scope.”

L'Enseignement mathématique

Graduate students, research mathematicians, educators, and mathematical physicists interested in functional analysis, operator algebras, and applications.

• Chapters
• Chapter 6. Comparison theory of projections
• Chapter 7. Normal states and unitary equivalence of von Neumann algebras
• Chapter 8. The trace
• Chapter 9. Algebra and commutant
• Chapter 10. Special representations of $C^*$-algebras
• Chapter 11. Tensor products
• Chapter 12. Approximation by matrix algebras
• Chapter 13. Crossed products
• Chapter 14. Direct integrals and decompositions
• Reviews

• What is presented here is an exciting and careful account of some very substantial mathematics! … As with the first volume, this book has an outstanding collection of exercises (and groupings of exercises) … Although the material in this second volume is substantially more advanced than that in the first volume, the authors have maintained the same spirit of freshness of the presentation given there.

Mathematical Reviews
• This book is extremely clear and well written and ideally suited for an introductory course on the subject or for a student who wishes to learn the fundamentals of the classical theory of operator algebras.

Zentralblatt MATH
• This volume by one of the co-founders of the isomorphism theory of Bernoulli processes offers a comprehensive treatment of finite-state stationary processes, with special emphasis on their combinatorial and coding properties. It is of interest to advanced graduate students and researchers working in ergodic theory, probability and information and gives an excellent account of many different tools and constructions of measure-theoretic dynamics … There is a useful bibliography which allows the interested reader to trace the history of the ideas presented in the book.

Monatshefte für Mathematik
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 161997; 676 pp
MSC: Primary 46; Secondary 47;

This work and Fundamentals of the Theory of Operator Algebras. Volume I, Elementary Theory present an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology. The book presents the possibility for the design of numerous courses aimed at different audiences.

Praise for both volumes …

“ …these two volumes represent a magnificent achievement. They will be an essential item on every operator algebraist's bookshelves and will surely become the primary source of instruction for research students in von Neumann algebra theory.”

Bulletin of the London Mathematical Society

“Volumes I and II were published in 1982 and 1983. Since then they have quickly established themselves as The Textbooks in operator algebra theory.”

Bulletin of the American Mathematical Society

“One of the splendid features of the original two volumes is their large supply of exercises … which illustrate the results of the text and expand its scope.”

L'Enseignement mathématique

Graduate students, research mathematicians, educators, and mathematical physicists interested in functional analysis, operator algebras, and applications.

• Chapters
• Chapter 6. Comparison theory of projections
• Chapter 7. Normal states and unitary equivalence of von Neumann algebras
• Chapter 8. The trace
• Chapter 9. Algebra and commutant
• Chapter 10. Special representations of $C^*$-algebras
• Chapter 11. Tensor products
• Chapter 12. Approximation by matrix algebras
• Chapter 13. Crossed products
• Chapter 14. Direct integrals and decompositions
• What is presented here is an exciting and careful account of some very substantial mathematics! … As with the first volume, this book has an outstanding collection of exercises (and groupings of exercises) … Although the material in this second volume is substantially more advanced than that in the first volume, the authors have maintained the same spirit of freshness of the presentation given there.

Mathematical Reviews
• This book is extremely clear and well written and ideally suited for an introductory course on the subject or for a student who wishes to learn the fundamentals of the classical theory of operator algebras.

Zentralblatt MATH
• This volume by one of the co-founders of the isomorphism theory of Bernoulli processes offers a comprehensive treatment of finite-state stationary processes, with special emphasis on their combinatorial and coding properties. It is of interest to advanced graduate students and researchers working in ergodic theory, probability and information and gives an excellent account of many different tools and constructions of measure-theoretic dynamics … There is a useful bibliography which allows the interested reader to trace the history of the ideas presented in the book.

Monatshefte für Mathematik
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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