Operator and Norm Inequalities and Related Topics (Trends in Mathematics) - Softcover

Softcover

ISBN 10: 3031021061 ISBN 13: 9783031021060

Publisher: Birkhäuser, 2024

Synopsis

Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades.

Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development.

A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. 

The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

About this title

About the Author

Richard M. Aron is Professor Emeritus of Mathematics at Kent State University, Ohio. Previously, he was a Lecturer and Fellow at Trinity College, University of Dublin. His research interests center on non-linear complex and functional analysis. He is an Editor in Chief of the Journal of Mathematical Analysis and Applications and is on the Editorial Board of the Mathematical Proceedings of the Royal Irish Academy and of RACSAM (Mathematical Journal of the Spanish Royal Academy of Sciences). He has been a Fulbright Fellow on several occasions (Bogota-Columbia, Buenos Aires-Argentina, and Dublin-Ireland).

Mohammad Sal Moslehian is a Professor of Mathematics at the Ferdowsi University of Mashhad, an invited member of the Academy of Sciences of Iran, and the President of the Iran. Math. Soc. His research concerns operator algebras, Hilbert C*-modules, in particular, operator and norm inequalities. He was a Senior Associate in ICTP (Italy) and a visiting professor atseveral universities in England, Sweden, and Japan. He is the editor-in-chief of the journals "Banach J. Math. Anal.", "Ann. Funct. Anal.", and "Adv. Oper. Theory" being published by Birkhäuser/Springer.

Ilya M. Spitkovsky is a Professor of Mathematics at the New York University Abu Dhabi campus (NYUAD) since 2013, having worked at the College of William and Mary for almost 25 years prior to that. His research is on the spectral theory of operators, numerical ranges and their generalizations, Wiener-Hopf and convolution type equations, and their applications. He is an author of three research monographs and served as an editor of eight more.

Hugo J. Woerdeman received his Ph.D. from the Vrije Universiteit in Amsterdam, The Netherlands in 1989. In that same year, he was appointed assistant professor at the College of William and Mary. During his tenure there he received a 1995 Alumni Fellowship Award for "Excellence in Teaching", and he was awarded the title of Margaret L. Hamilton Professor of Mathematics. In December 2004 he joined Drexel University as Professor and Department Head. Over the years, he has had long-term stays at the University of California, San Diego, the George Washington University, Ecole Nationale Superieure des Techniques Avancees, Katholieke Universiteit Leuven, Universite Catholique de Louvain, Princeton University, and the University of Waterloo.

From the Back Cover

Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades.

Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development.

A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. 

The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

Edition details

• Publisher: Birkhäuser
• Publication date: 2024
• Language: English
• ISBN 10: 3031021061
• ISBN 13: 9783031021060
• Binding: Paperback
• Number of pages: 835
• Editor: Aron Richard M., Moslehian Mohammad Sal, Spitkovsky Ilya M., Woerdeman Hugo J.