Overview
- Analyzes the norm structure through algebraic approaches with geometric visualization
- Focuses on topics in geometry of operator spaces through Birkhoff–James orthogonality
- Covers a vast area of geometric notions in the space of bounded linear operators
Part of the book series: Infosys Science Foundation Series (ISFS)
Part of the book sub series: Infosys Science Foundation Series in Mathematical Sciences (ISFM)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (8 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
This book provides an insight into the geometric aspects of the spaces of operators studied by using the notion of Birkhoff–James orthogonality. It studies the norm attainment set of an operator and its properties, the notion of which plays a very important role in the characterization of B-J orthogonality of operators. The structure of the norm attainment set is studied for Hilbert space operators and is yet to be understood completely for operators between Banach spaces. The book explores the interrelation between B-J orthogonality in the ground space and in the space of operators in its fullest generality. The book further explores the concept of approximate B-J orthogonality and investigated its geometry both in the ground space as well as in the space of operators. It highlights important geometric properties like smoothness and k-smoothness of bounded linear operators, extreme contractions and symmetricity of bounded linear operators defined between Hilbert spaces as well as Banach spaces.
Authors and Affiliations
About the authors
Kallol Paul is a Professor at the Department of Mathematics, Jadavpur University, Kolkata. He completed his B.Sc. in Mathematics from Gauhati University, Assam, and M.Sc. from Jadavpur University, securing the first-class-first position in both the examinations. His broad area of research is functional analysis and operator theory. With more than 26 years of teaching and research experience, he has so far guided 16 students for the successful completion of their Ph.D. degrees, and another 6 students are presently pursuing their doctoral research under his supervision. He has published more than 140 papers in various international journals of repute. His current area of teaching includes real analysis, metric spaces, and operator theory. Presently, he is actively involved in research on a variety of topics, including numerical radius inequalities, Birkhoff–James orthogonality, and its applications in the study of Banach spaces. With a vast international network of collaborators, Prof. Paul has played a crucial role in establishing Jadavpur University as an important center of research activity on Banach space theory.
Debmalya Sain is an Assistant Professor at the Department of Mathematics and Computing, Indian Institute of Information Technology Raichur, Karnataka, India. An alumnus of Ramakrishna Mission Vidyapith, Purulia, he completed his Ph.D. degree in 2015 under the guidance of Prof. Kallol Paul. A recipient of multiple Gold Medals in his undergraduate and postgraduate studies, Dr. Sain stood first-class-first in both his B.Sc. and M.Sc. examinations at Jadavpur University, Kolkata. He completed multiple post-doctoral fellowships at the Indian Institute of Science, Bengaluru, under the mentorship of Prof. Gadadhar Misra and Prof. Apoorva Khare. He has also received many international grants and awards, including the prestigious Maria Zambrano grant to pursue his research at the Universidad de Granada, Spain, under the guidance of Prof. Miguel Martin. Dr. Sain has authored more than 75 articles in various reputed international journals. Apart from acting as a referee and reviewer for many international journals, he is an invited member of the editorial board of the Advances in Operator Theory journal, published by Birkhauser.
Bibliographic Information
Book Title: Birkhoff–James Orthogonality and Geometry of Operator Spaces
Authors: Arpita Mal, Kallol Paul, Debmalya Sain
Series Title: Infosys Science Foundation Series
DOI: https://doi.org/10.1007/978-981-99-7111-4
Publisher: Springer Singapore
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 Singapore Pte Ltd. 2024
Hardcover ISBN: 978-981-99-7110-7Published: 20 February 2024
Softcover ISBN: 978-981-99-7113-8Due: 22 March 2024
eBook ISBN: 978-981-99-7111-4Published: 19 February 2024
Series ISSN: 2363-6149
Series E-ISSN: 2363-6157
Edition Number: 1
Number of Pages: XIII, 251
Number of Illustrations: 9 b/w illustrations, 4 illustrations in colour
Topics: Operator Theory, Geometry, Functional Analysis