This book is a comprehensive and advanced exploration of trace inequalities in the context of matrices and operators acting on Hilbert spaces. Its goal is to present elegant inequalities with innovative proofs. Instead of presenting generalized versions that can be complicated and lack clarity, the book focuses on beautiful and original inequalities. Divided into eight chapters, this book is designed for researchers and graduate students in mathematics, physics, and engineering. It provides detailed explanations for most of the results and includes a variety of exercises and problems to help readers understand the content and inspire further research into advanced topics.

Presents a comprehensive and advanced account of trace inequalities in complex matrices and operators on Hilbert spaces Introduces several active research areas in matrix analysis and operator theory Includes elegant inequalities with ingenious proofs and presents beautiful and original inequalities

Autorentext

Airat Midkhatovich Bikchentaev is a professor at the Lobachevskii Institute of Mathematics and Mechanics, Kazan Federal University (Volga Region), Kazan, Russia. Previously, he served as a visiting professor at several universities in Kazakhstan and Uzbekistan. He received the Kandidat Nauk (Ph.D.) in 1990 and Doctor Nauk (Dr.Sc.) in 2012. He was a leading researcher at the Mathematical Center of the Volga Region of the Russian Federation, and his research concerns functional analysis, operator theory, and matrix analysis. In 1993, he was supported by a grant from the French Mathematical Society. From 2008 to 2021, he was the deputy editor-in-chief of the Russian Mathematics journal, published by Springer. He is also an editor of the Advances in Operator Theory journal. Fuad Kittaneh is a professor in the Department of Mathematics at the University of Jordan, where he has also held various administrative positions. After receiving his Ph.D. from Indiana University, USA, in 1982, he has worked at several universities in Jordan and other countries. His research fields are functional analysis, operator theory, and matrix analysis. He has been invited to give talks at several international universities and research centers. He is on the editorial boards of several prestigious mathematical journals such as the Banach Journal of Mathematical Analysis, Complex Analysis and Operator Theory, The Electronic Journal of Linear Algebra, and Operators and Matrices. Mohammad Sal Moslehian is a professor in the Department of Pure Mathematics at Ferdowsi University of Mashhad, Iran. He is a member of the Academy of Sciences of Iran and a TWAS fellow. His research fields include functional analysis, operator theory, and matrix analysis. Earlier, he was a senior associate at ICTP in Italy, and a visiting professor at various universities in the UK, Sweden, and Japan. He serves as the founder and editor-in-chief of the following Springer journals: Banach Journal of Mathematical Analysis, Annals of Functional Analysis, and Advances in Operator Theory. Yuki Seo is a professor of Mathematics Education at Osaka Kyoiku University, Japan. He is a member of the Mathematical Society of Japan, and his research concerns functional analysis, operator theory, and matrix analysis. He is an editor of the Annals of Functional Analysis and the Journal of Mathematical Inequalities.

Inhalt

Chapter 1 Fundamentals of Matrices and Operators.- Chapter 2 Unitarily Invariant Norms and Inequalities.- Chapter 3 Trace Inequalities for Positive Semidefinite Matrices.- Chapter 4 Norm Inequalities for Positive Semidefinite Matrices.- Chapter 5 Positive Maps and Operator Means.