Trace Inequalities

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.

“This monograph offers a nice and unified treatment of trace inequalities that cuts across pure mathematics and quantum theory. With clear exposition, strong motivation, and extensive bibliographic support, it is a valuable addition to the literature. Exercises, commentary, and hints add to its pedagogical strength. It will serve as a valuable reference for specialists and a high-level teaching resource.” (Tin Yau Tam, zbMATH 1569.15002, 2026)

• 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.