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Positive Definiteness of Functions with Applications to Operator Norm Inequalities
eBook ISBN:  9781470406141 
Product Code:  MEMO/212/997.E 
List Price:  $70.00 
MAA Member Price:  $63.00 
AMS Member Price:  $42.00 
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Positive Definiteness of Functions with Applications to Operator Norm Inequalities
eBook ISBN:  9781470406141 
Product Code:  MEMO/212/997.E 
List Price:  $70.00 
MAA Member Price:  $63.00 
AMS Member Price:  $42.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 212; 2011; 80 ppMSC: 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 Heinztype 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 Herontype 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


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 Book Details
 Table of Contents
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Volume: 212; 2011; 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 Heinztype 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 Herontype 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
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