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Completely Bounded Maps and Operator Algebras

Completely Bounded Maps and Operator Algebras


Part of Cambridge Studies in Advanced Mathematics

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

£ 103.00

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About the Authors
  • In this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since 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 indispensable introduction to the theory of operator spaces for all who want to know more.

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

    'This book has been written by one of the leading figures in the field. the choice of the presented material has been done in a masterly manner … an excellent introduction to this theory for graduate students. It should also provide a valuable reference source for researchers in the field.' Zentralblatt für Mathematik

    'The book is carefully written, proofs are often accompanied with notes helping to explain the situation.' EMS Newsletter

    'Paulsen's book has the advantage of still being concise and staying close to the origins of the theory … the subject of operator spaces is now very well covered and has been made accessible to both the newcomer to the subject, and the specialist looking for concise references, alike. In conclusion, we quote from the cover text of [2]: 'This will be an indispensable introduction to the theory of operator spaces for all who want to know more.' We add: you surely will want to know more.' Martin Mathieu, Queen's University Belfast

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    Product details

    • Date Published: February 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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    Vern Paulsen, University of Houston

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