Memoirs of the American Mathematical Society 2011; 80 pp; softcover Volume: 212 ISBN10: 0821853074 ISBN13: 9780821853078 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. Table of Contents  Introduction
 Preliminaries
 Fourier transforms and positive definiteness
 A certain Heinztype 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 Herontype 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
