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Hilbert Modules over Operator Algebras
 
Paul S. Muhly University of Iowa
Baruch Solel Technion-Israel Inst of Tech
Hilbert Modules over Operator Algebras
eBook ISBN:  978-1-4704-0138-2
Product Code:  MEMO/117/559.E
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $20.40
Hilbert Modules over Operator Algebras
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Hilbert Modules over Operator Algebras
Paul S. Muhly University of Iowa
Baruch Solel Technion-Israel Inst of Tech
eBook ISBN:  978-1-4704-0138-2
Product Code:  MEMO/117/559.E
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $20.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1171995; 53 pp
    MSC: Primary 47; 46;

    This book gives a general systematic analysis of the notions of “projectivity” and “injectivity” in the context of Hilbert modules over operator algebras. A Hilbert module over an operator algebra \(A\) is simply the Hilbert space of a (contractive) representation of \(A\) viewed as a module over \(A\) in the usual way.

    In this work, Muhly and Solel introduce various notions of projective Hilbert modules and use them to investigate dilation and commutant lifting problems over certain infinite dimensional analogues of incidence algebras.

    The authors prove that commutant lifting holds for such an algebra if and only if the pattern indexing the algebra is a “tree” in the sense of computer directories.

    Readership

    Researchers in operator algebra.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Definitions
    • 3. Basic theory
    • 4. Incidence algebras and generalizations
    • Appendix
    • 5. Trees and trees
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1171995; 53 pp
MSC: Primary 47; 46;

This book gives a general systematic analysis of the notions of “projectivity” and “injectivity” in the context of Hilbert modules over operator algebras. A Hilbert module over an operator algebra \(A\) is simply the Hilbert space of a (contractive) representation of \(A\) viewed as a module over \(A\) in the usual way.

In this work, Muhly and Solel introduce various notions of projective Hilbert modules and use them to investigate dilation and commutant lifting problems over certain infinite dimensional analogues of incidence algebras.

The authors prove that commutant lifting holds for such an algebra if and only if the pattern indexing the algebra is a “tree” in the sense of computer directories.

Readership

Researchers in operator algebra.

  • Chapters
  • 1. Introduction
  • 2. Definitions
  • 3. Basic theory
  • 4. Incidence algebras and generalizations
  • Appendix
  • 5. Trees and trees
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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