#### Pregled bibliografske jedinice broj: 207801

## Mond-Pečarić Method in Operator Inequalities

Mond-Pečarić Method in Operator Inequalities, Zagreb: Element, 2005 (monografija)

**Naslov**

Mond-Pečarić Method in Operator Inequalities

**Autori**

Furuta, Takayuki ; Mićić, Jadranka ; Pečarić, Josip ; Seo, Yuki

**Vrsta, podvrsta i kategorija knjige**

Autorske knjige, monografija, znanstvena

**Izdavač**

Element

**Grad**

Zagreb

**Godina**

2005

**Stranica**

262

**ISBN**

953-197-572-8

**Ključne riječi**

Mond-Pečarić method; operator inequality; Jensen inequality; operator means; Hadamard product; Furuta inequality; operator order; chaotic order

**Sažetak**

In Chapter 1 a very brief and rapid review of some basic topics in Jensen's inequality for positive linear maps and Kantorovich inequality for several types are given. Some basic ideas and the viewpoints of the Mond-Pečerić method are given. In Chapter 2 general converses of Jensen's inequality are considered. The Mond-Pečerić method is used to obtain the bounds. Many interesting inequalities are particularly considered. In Chapter 3 a generalization of a theorem of Li-Mathias for the normalized positive linear maps as an application of the Mond-Pečerić method is considered. Lower and upper bounds in converses of Jensen's type inequalities are given. The cases of the sharp inequalities are investigated. The conversions of Jensen's inequality and other inequalities are particularly considered. In Chapter 4 the previous results and the same methods are applied to obtain the inequalities for the means. Reverse inequalities of power operator means on positive linear maps are studied. Several properties of power operator means under the chaotic order are considered. New bounds in inequalities for power operator means are given. In chapter 5 the theory of operator means established by Kubo and Ando assocaiated with the operator monotone functions is introduced. Based on complementary inequalities to Jensen's inequalities on positive linear maps, complementary inequalities to Ando's inequalities assocaiated with operator means are studied. In Chapter 6 the results and the same methods in the chapter 2 are applied to obtain the inequalities for the Hadamard product. Then the reverses inequalities on the Hadamard product of operators and operator means are considered. General inequalities for the Hadamard product of operators are observed. In chapter 7 a brief survey of several applications of both Furuta inequality and generalized Furuta inequality is given. In Chapter 8 the claims preserving the operator order and the chaotic order are considered as an application of the Mond-Pečerić method. The overall results on the functions which preserve the operator order and the chaotic order are particularly considered.

**Izvorni jezik**

Engleski

**Znanstvena područja**

Matematika