Advances in Matrix Inequalities

This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.

Detailed proofs for all the main theorems and relevant technical lemmas are presented Accessible to researchers, graduate students, engineers, physicists, economists Unifies theorems and applications

Auteur

Mohammad Bagher Ghaemi is an associate professor of mathematics at the Iran University of Science and Technology, Tehran. His research interests include operator theory, nonlinear analysis, approximation theory, functional analysis, functional equations, inequalities and applications. Professor Ghaemi received his PhD in mathematics from Glasgow University, Scotland, in 2000; his PhD advisor was P.G. Spain. He has published more than 60 papers. Nahid Gharakhanlu received her PhD in pure mathematics from the Iran University of Science and Technology, Tehran in 2017. Her PhD advisor was Mohammad Bagher Ghaemi. Her research interests include matrix analysis, functional analysis, operator theory, linear algebra, inequalities and their applications. Themistocles M. Rassias is professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Professor Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, Professor Rassias has published as author or volume editor several books published with Springer. Th. M. Rassias has received several awards and is an active editorial board member of an array of journals in mathematical analysis and optimization. His publications have received a large number of citations, with h-index 46. Reza Saadati is a member of the mathematics department of the Iran University of Science and Technology, Tehran. His research interests include nonlinear analysis and applications. Professor Saadati received his PhD in mathematics from Amirkabir University of Technology, in 2010; his PhD advisor was S. M. Vaezpour. He has published several books with Springer.

Résumé

"The book is written in a readable style and provides several interesting and nice techniques. It is very useful for graduate students and researchers interested in operator and norm inequalities." (Mohammad Sal Moslehian, Mathematical Reviews, June, 2023)

The book contains a bibliography of over 200 items and ... the many inequalities presented, usually with full proofs provided. ... if you are looking for an inequality in the areas covered, then this should be a useful source." (John D. Dixon, zbMATH 1477.15001, 2022)

Contenu

1. Elementary linear algebra review.- 2. Interpolating the arithmetic-geometric mean inequality and its operator version.- 3. Operator inequalities for positive linear maps.- 4. Operator inequalities involving operator monotone functions.- 5. Inequalities for sector matrices.- 6. Positive partial transpose matrix inequalities.- References.- Index.