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Softcover ISBN:  9780821852545 
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Softcover ISBN:  9780821852545 
Product Code:  ULECT/56 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470416515 
Product Code:  ULECT/56.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821852545 
eBook ISBN:  9781470416515 
Product Code:  ULECT/56.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

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.

Table of Contents

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


Additional Material

Reviews

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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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