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| Softcover ISBN: | 978-0-8218-5254-5 |
| Product Code: | ULECT/56 |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| eBook ISBN: | 978-1-4704-1651-5 |
| Product Code: | ULECT/56.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $52.00 |
| Softcover ISBN: | 978-0-8218-5254-5 |
| eBook ISBN: | 978-1-4704-1651-5 |
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| List Price: | $134.00 $101.50 |
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Book DetailsUniversity Lecture SeriesVolume: 56; 2010; 241 ppMSC: Primary 46; 47
This book contains a systematic presentation of quantum functional analysis, a mathematical subject also known as operator space theory. Created in the 1980s, it nowadays is one of the most prominent areas of functional analysis, both as a field of active research and as a source of numerous important applications.
The approach taken in this book differs significantly from the standard approach used in studying operator space theory. Instead of viewing “quantized coefficients” as matrices in a fixed basis, in this book they are interpreted as finite rank operators in a fixed Hilbert space. This allows the author to replace matrix computations with algebraic techniques of module theory and tensor products, thus achieving a more invariant approach to the subject.
The book can be used by graduate students and research mathematicians interested in functional analysis and related areas of mathematics and mathematical physics. Prerequisites include standard courses in abstract algebra and functional analysis.
ReadershipGraduate students and research mathematicians interested in functional analysis.
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Table of Contents
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Chapters
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Chapter 0. Three basic definitions and three principal theorems
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Part I. The beginning: Spaces and operators
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Chapter 1. Preparing the stage
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Chapter 2. Abstract operator ( = quantum) spaces
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Chapter 3. Completely bounded operators
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Chapter 4. The completion of abstract operator spaces
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Part II. Bilinear operators, tensor products and duality
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Chapter 5. Strongly and weakly completely bounded bilinear operators
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Chapter 6. New preparations: Classical tensor products
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Chapter 7. Quantum tensor products
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Chapter 8. Quantum duality
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Part III. Principal theorems, revisited in earnest
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Chapter 9. Extreme flatness and the extension theorem
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Chapter 10. Representation theorem and its gifts
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Chapter 11. Decomposition theorem
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Chapter 12. Returning to the Haagerup tensor product
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Chapter 13. Miscellany: More examples, facts and applications
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Additional Material
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Reviews
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This book is highly recommended to mathematicians who wish to become acquainted with the research field of operator spaces, operator modules and operator algebras.
Mathematical Reviews
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
This book contains a systematic presentation of quantum functional analysis, a mathematical subject also known as operator space theory. Created in the 1980s, it nowadays is one of the most prominent areas of functional analysis, both as a field of active research and as a source of numerous important applications.
The approach taken in this book differs significantly from the standard approach used in studying operator space theory. Instead of viewing “quantized coefficients” as matrices in a fixed basis, in this book they are interpreted as finite rank operators in a fixed Hilbert space. This allows the author to replace matrix computations with algebraic techniques of module theory and tensor products, thus achieving a more invariant approach to the subject.
The book can be used by graduate students and research mathematicians interested in functional analysis and related areas of mathematics and mathematical physics. Prerequisites include standard courses in abstract algebra and functional analysis.
Graduate students and research mathematicians interested in functional analysis.
-
Chapters
-
Chapter 0. Three basic definitions and three principal theorems
-
Part I. The beginning: Spaces and operators
-
Chapter 1. Preparing the stage
-
Chapter 2. Abstract operator ( = quantum) spaces
-
Chapter 3. Completely bounded operators
-
Chapter 4. The completion of abstract operator spaces
-
Part II. Bilinear operators, tensor products and duality
-
Chapter 5. Strongly and weakly completely bounded bilinear operators
-
Chapter 6. New preparations: Classical tensor products
-
Chapter 7. Quantum tensor products
-
Chapter 8. Quantum duality
-
Part III. Principal theorems, revisited in earnest
-
Chapter 9. Extreme flatness and the extension theorem
-
Chapter 10. Representation theorem and its gifts
-
Chapter 11. Decomposition theorem
-
Chapter 12. Returning to the Haagerup tensor product
-
Chapter 13. Miscellany: More examples, facts and applications
-
This book is highly recommended to mathematicians who wish to become acquainted with the research field of operator spaces, operator modules and operator algebras.
Mathematical Reviews
