Kosaki H. Positive definiteness of functions with applications to operator norm inequalities. - Providence: American Mathematical Society, 2011. - v, 80 p. - (Memoirs of the American Mathematical Society; vol.212, N 997). - Bibliogr.: p.77-78. - Ind.: p.79-80. - ISBN 978-0-8218-5307-8; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Chapter 1. Introduction ......................................... 1 Chapter 2. Preliminaries ........................................ 7 Chapter 3. Fourier transforms and positive definiteness ........ 13 3.1. Sinh(αt) ............................................ 13 cosh t 3.2. cosh(αt)sinh(βt) ................................... 15 cosh t 3.3. Sinh(αt)cosh(βt) and Sinh(αt)sinh(βt) .............. 17 sinh t sinh t 3.4. cosh(Παt) and sinh(Παt) ........................ 19 cosh2(Πt/2) cosh2(Πt/2) 3.5. t cosh(αt) and t sinh(αt) .......................... 22 sinh t sinh t 3.6. t(cosh(αt) + β) ...................................... 23 sinh t 3.7. t(cosh(βt) + γ)sinh(αt) .............................. 27 sinh t 3.8. t(cosh(βt) + γ)cosh(αt) .............................. 31 cosh t Chapter 4. A certain Heinz-type inequality and related commutator estimates ................................ 37 4.1. A certain Heinz-type inequality and its consequences ... 37 4.2. Certain commutator estimates ........................... 40 Chapter 5. Norm comparison for various operator means .......... 43 5.1. Heinz and A-L-G interpolation means .................... 43 5.2. Heinz means and the binomial mean B1/2 .................. 46 Chapter 6. Norm inequalities for H1/2+βXK1/2-β + H1/2-βXK1/2+β ± H1/2XK1/2 ............................................ 49 6.1. Comparison to the logarithmic mean ..................... 49 6.2. Comparison to A-L-G interpolation means ................ 50 Chapter 7. Norm comparison of Heron-type means and related topics .............................................. 55 7.1. Criterion for positive definiteness .................... 55 7.2. Heron-type means and a one-parameter version of Heinz inequality ............................................. 59 7.3. Miscellaneous results .................................. 61 Chapter 8. Operator Lehmer means and their properties .......... 65 Appendix A. A direct proof for Proposition 7.3 ................. 69 Appendix B. Proof for Theorem 7.10 ............................. 73 Bibliography ................................................... 77 Index .......................................................... 79