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!
Positive Definiteness of Functions with Applications to Operator Norm Inequalities
 
Hideki Kosaki Kyushu University, Fukuoka, Japan
Positive Definiteness of Functions with Applications to Operator Norm Inequalities
eBook ISBN:  978-1-4704-0614-1
Product Code:  MEMO/212/997.E
List Price: $70.00
MAA Member Price: $63.00
AMS Member Price: $42.00
Positive Definiteness of Functions with Applications to Operator Norm Inequalities
Click above image for expanded view
Positive Definiteness of Functions with Applications to Operator Norm Inequalities
Hideki Kosaki Kyushu University, Fukuoka, Japan
eBook ISBN:  978-1-4704-0614-1
Product Code:  MEMO/212/997.E
List Price: $70.00
MAA Member Price: $63.00
AMS Member Price: $42.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2122011; 80 pp
    MSC: Primary 47; Secondary 15;

    Positive definiteness is determined for a wide class of functions relevant in the study of operator means and their norm comparisons. Then, this information is used to obtain an abundance of new sharp (unitarily) norm inequalities comparing various operator means and sometimes other related operators.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Fourier transforms and positive definiteness
    • 4. A certain Heinz-type inequality and related commutator estimates
    • 5. Norm comparison for various operator means
    • 6. Norm inequalities for $H^{\frac {1}{2}+\beta }XK^{\frac {1}{2}-\beta }+ H^{\frac {1}{2}-\beta }XK^{\frac {1}{2}+\beta }\pm H^{1/2}XK^{1/2}$
    • 7. Norm comparison of Heron-type means and related topics
    • 8. Operator Lehmer means and their properties
    • A. A direct proof for Proposition 7.3
    • B. Proof for Theorem 7.10
  • 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: 2122011; 80 pp
MSC: Primary 47; Secondary 15;

Positive definiteness is determined for a wide class of functions relevant in the study of operator means and their norm comparisons. Then, this information is used to obtain an abundance of new sharp (unitarily) norm inequalities comparing various operator means and sometimes other related operators.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Fourier transforms and positive definiteness
  • 4. A certain Heinz-type inequality and related commutator estimates
  • 5. Norm comparison for various operator means
  • 6. Norm inequalities for $H^{\frac {1}{2}+\beta }XK^{\frac {1}{2}-\beta }+ H^{\frac {1}{2}-\beta }XK^{\frac {1}{2}+\beta }\pm H^{1/2}XK^{1/2}$
  • 7. Norm comparison of Heron-type means and related topics
  • 8. Operator Lehmer means and their properties
  • A. A direct proof for Proposition 7.3
  • B. Proof for Theorem 7.10
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.