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Quantum Functional Analysis: Non-Coordinate Approach

About this Title

A. Ya. Helemskii, Moscow Lomonosov State University, Moscow, Russia

Publication: University Lecture Series
Publication Year: 2010; Volume 56
ISBNs: 978-0-8218-5254-5 (print); 978-1-4704-1651-5 (online)
DOI: https://doi.org/10.1090/ulect/056
MathSciNet review: MR2760416
MSC: Primary 46L07; Secondary 46H25, 46M05, 46N50, 47L25, 47N50

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Table of Contents

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Front/Back Matter

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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