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Completely Bounded Maps and Operator Algebras

Completely Bounded Maps and Operator Algebras

$145.00 (C)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: April 2003
  • availability: Available
  • format: Hardback
  • isbn: 9780521816694

$ 145.00 (C)

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About the Authors
  • This book tours the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis. The presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will appreciate how the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensible introduction to the theory of operator spaces.

    •  Self-contained
    • Author is an excellent expositor
    •  First real introduction to the subject for graduate students
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    Reviews & endorsements

    "Although it contains deep and advanced results on operator spaces and their applications, the book is essentially self-contained and accessible to anyone with a basic knowledge in general functional analysis and C*-algebras." Mathematical Reviews

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    Product details

    • Date Published: April 2003
    • format: Hardback
    • isbn: 9780521816694
    • length: 314 pages
    • dimensions: 161 x 234 x 21 mm
    • weight: 0.53kg
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Positive maps
    3. Completely positive maps
    4. Dilation theorems
    5. Commuting contractions
    6. Completely positive maps into Mn
    7. Arveson's extension theorems
    8. Completely bounded maps
    9. Completely bounded homomorphisms
    10. Polynomially bounded operators
    11. Applications to K-spectral sets
    12. Tensor products and joint spectral sets
    13. Operator systems and operator spaces
    14. An operator space bestiary
    15. Injective envelopes
    16. Multipliers and operator algebras
    17. Completely bounded multilinear maps
    18. Applications of operator algebras
    19. Similarity and factorization degree.

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    Completely Bounded Maps and Operator Algebras

    Vern Paulsen

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  • Author

    Vern Paulsen, University of Houston

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