Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
 
Gilles Pisier Texas A&M University, College Station, TX and University of Paris VI, France
The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
eBook ISBN:  978-1-4704-0170-2
Product Code:  MEMO/122/585.E
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
Click above image for expanded view
The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
Gilles Pisier Texas A&M University, College Station, TX and University of Paris VI, France
eBook ISBN:  978-1-4704-0170-2
Product Code:  MEMO/122/585.E
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1221996; 103 pp
    MSC: Primary 46

    In the recently developed duality theory of operator spaces (as developed by Effros-Ruan and Blecher-Paulsen) bounded operators are replaced by completely bounded ones, isomorphisms by complete isomorphisms, and Banach spaces by operator spaces. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into \(B(H)\) (with \(H\) being Hilbert). In this new category, several operator spaces which are isomorphic (as Banach spaces) to a Hilbert space play an important role. For instance the row and column Hilbert spaces and several other examples appearing naturally in the construction of the Boson or Fermion Fock spaces have been studied extensively.

    One of the main results of this memoir is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (denoted by \(OH\) ) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces.

    This new concept, called “the operator Hilbert space” and denoted by \(OH\), is introduced and thoroughly studied in this volume.

    Readership

    Graduate students and research mathematicians interested in functional analysis.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. The operator Hilbert space
    • 2. Complex interpolation
    • 3. The $oh$ tensor product
    • 4. Weights on partially ordered vector spaces
    • 5. (2,$w$)-summing operators
    • 6. The gamma-norms and their dual norms
    • 7. Operators factoring through $OH$
    • 8. Factorization through a Hilbertian operator space
    • 9. On the “local theory” of operator spaces
    • 10. Open questions
  • 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: 1221996; 103 pp
MSC: Primary 46

In the recently developed duality theory of operator spaces (as developed by Effros-Ruan and Blecher-Paulsen) bounded operators are replaced by completely bounded ones, isomorphisms by complete isomorphisms, and Banach spaces by operator spaces. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into \(B(H)\) (with \(H\) being Hilbert). In this new category, several operator spaces which are isomorphic (as Banach spaces) to a Hilbert space play an important role. For instance the row and column Hilbert spaces and several other examples appearing naturally in the construction of the Boson or Fermion Fock spaces have been studied extensively.

One of the main results of this memoir is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (denoted by \(OH\) ) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces.

This new concept, called “the operator Hilbert space” and denoted by \(OH\), is introduced and thoroughly studied in this volume.

Readership

Graduate students and research mathematicians interested in functional analysis.

  • Chapters
  • Introduction
  • 1. The operator Hilbert space
  • 2. Complex interpolation
  • 3. The $oh$ tensor product
  • 4. Weights on partially ordered vector spaces
  • 5. (2,$w$)-summing operators
  • 6. The gamma-norms and their dual norms
  • 7. Operators factoring through $OH$
  • 8. Factorization through a Hilbertian operator space
  • 9. On the “local theory” of operator spaces
  • 10. Open questions
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
Please select which format for which you are requesting permissions.