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!
Operator-Valued Measures, Dilations, and the Theory of Frames
 
Deguang Han University of Central Florida, Orlando, Florida
David R. Larson Texas A&M University, College Station, Texas
Bei Liu Tianjin University of Technology, Tianjin, China
Rui Liu Nankai University , Tianjuin, China
Operator-Valued Measures, Dilations, and the Theory of Frames
eBook ISBN:  978-1-4704-1529-7
Product Code:  MEMO/229/1075.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $39.00
Operator-Valued Measures, Dilations, and the Theory of Frames
Click above image for expanded view
Operator-Valued Measures, Dilations, and the Theory of Frames
Deguang Han University of Central Florida, Orlando, Florida
David R. Larson Texas A&M University, College Station, Texas
Bei Liu Tianjin University of Technology, Tianjin, China
Rui Liu Nankai University , Tianjuin, China
eBook ISBN:  978-1-4704-1529-7
Product Code:  MEMO/229/1075.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $39.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2292013; 84 pp
    MSC: Primary 46; 47; Secondary 42

    The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation results for bounded linear maps that are not necessarily completely bounded, and from domain algebras that are not necessarily abelian. In the non-cb case the dilation space often needs to be a Banach space. They give applications to both the discrete and the continuous frame theory. There are natural associations between the theory of frames (including continuous frames and framings), the theory of operator-valued measures on sigma-algebras of sets, and the theory of continuous linear maps between \(C^*\)-algebras. In this connection frame theory itself is identified with the special case in which the domain algebra for the maps is an abelian von Neumann algebra and the map is normal (i.e. ultraweakly, or \(\sigma\) weakly, or w*) continuous.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Preliminaries
    • 2. Dilation of Operator-valued Measures
    • 3. Framings and Dilations
    • 4. Dilations of Maps
    • 5. Examples
  • 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: 2292013; 84 pp
MSC: Primary 46; 47; Secondary 42

The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation results for bounded linear maps that are not necessarily completely bounded, and from domain algebras that are not necessarily abelian. In the non-cb case the dilation space often needs to be a Banach space. They give applications to both the discrete and the continuous frame theory. There are natural associations between the theory of frames (including continuous frames and framings), the theory of operator-valued measures on sigma-algebras of sets, and the theory of continuous linear maps between \(C^*\)-algebras. In this connection frame theory itself is identified with the special case in which the domain algebra for the maps is an abelian von Neumann algebra and the map is normal (i.e. ultraweakly, or \(\sigma\) weakly, or w*) continuous.

  • Chapters
  • Introduction
  • 1. Preliminaries
  • 2. Dilation of Operator-valued Measures
  • 3. Framings and Dilations
  • 4. Dilations of Maps
  • 5. Examples
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.