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  • © 2022

Operator and Norm Inequalities and Related Topics

Birkhäuser
  • Includes contributions by a number of the world's leading specialists in functional analysis and operator theory

  • Presents some of the latest developments in operator theory

  • Introduces several active research areas within operator theory and its applications

Part of the book series: Trends in Mathematics (TM)

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-xiii
  2. Matrix and Operator Inequalities

    1. Front Matter

      Pages 1-1
    2. Log-majorization Type Inequalities

      • N. Bebiano, R. Lemos, G. Soares
      Pages 3-40
    3. Ando-Hiai Inequality: Extensions and Applications

      • Masatoshi Fujii, Ritsuo Nakamoto
      Pages 41-67
    4. Relative Operator Entropy

      • Jun Ichi Fujii, Yuki Seo
      Pages 69-95
    5. Matrix Inequalities and Characterizations of Operator Monotone Functions

      • Trung Hoa Dinh, Hiroyuki Osaka, Oleg E. Tikhonov
      Pages 97-130
    6. Perspectives, Means and their Inequalities

      • Hiroyuki Osaka, Shuhei Wada
      Pages 131-178
  3. Orthogonality and Inequalities

    1. Front Matter

      Pages 253-253
    2. Birkhoff–James Orthogonality: Characterizations, Preservers, and Orthogonality Graphs

      • Ljiljana Arambašić, Alexander Guterman, Bojan Kuzma, Svetlana Zhilina
      Pages 255-302
    3. Orthogonally Additive Operators on Vector Lattices

      • Marat Pliev, Mikhail Popov
      Pages 321-351
  4. Inequalities Related to Types of Operators

    1. Front Matter

      Pages 353-353
    2. Normal Operators and their Generalizations

      • Pietro Aiena
      Pages 355-396
    3. On Wold Type Decomposition for Closed Range Operators

      • H. Ezzahraoui, M. Mbekhta, E. H. Zerouali
      Pages 397-427
    4. (Asymmetric) Dual Truncated Toeplitz Operators

      • M. Cristina Câmara, Kamila Kliś-Garlicka, Marek Ptak
      Pages 429-460
    5. Boundedness of Toeplitz Operators in Bergman-Type Spaces

      • Jari Taskinen, Jani A. Virtanen
      Pages 461-490
  5. Inequalities in Various Banach Spaces

    1. Front Matter

      Pages 491-491
    2. Disjointness Preservers and Banach-Stone Theorems

      • Denny H. Leung, Wee Kee Tang
      Pages 493-518

About this book

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.

Editors and Affiliations

  • Department of Mathematical Sciences, Kent State University, Kent, USA

    Richard M. Aron

  • Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

    Mohammad Sal Moslehian

  • Department of Mathematics, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

    Ilya M. Spitkovsky

  • Department of Mathematics, Drexel University, Philadelphia, USA

    Hugo J. Woerdeman

About the editors

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 at several 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.

Bibliographic Information

  • Book Title: Operator and Norm Inequalities and Related Topics

  • Editors: Richard M. Aron, Mohammad Sal Moslehian, Ilya M. Spitkovsky, Hugo J. Woerdeman

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-02104-6

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-02103-9Published: 11 August 2022

  • Softcover ISBN: 978-3-031-02106-0Due: 25 August 2023

  • eBook ISBN: 978-3-031-02104-6Published: 10 August 2022

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: XIII, 822

  • Number of Illustrations: 5 b/w illustrations, 4 illustrations in colour

  • Topics: Operator Theory

Buy it now

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 159.99
Price excludes VAT (USA)
This title has not yet been released. You may pre-order it now and we will ship your order when it is published on 22 Sep 2023.
  • Compact, lightweight edition
  • Free shipping worldwide - see info
Hardcover Book USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access