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Positive Definiteness of Functions with Applications to Operator Norm Inequalities
Hideki Kosaki, Kyushu University, Fukuoka, Japan
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Memoirs of the American Mathematical Society
2011; 80 pp; softcover
Volume: 212
ISBN-10: 0-8218-5307-4
ISBN-13: 978-0-8218-5307-8
List Price: US$66 Individual Members: US$39.60
Institutional Members: US\$52.80
Order Code: MEMO/212/997

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.

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