Birkhoff-James Orthogonality and Geometry of Operator Spaces

本書透過使用 Birkhoff-James 正交性的概念，提供了對運算子空間的幾何方面的深入洞察。它研究了運算子的範數達成集及其性質，這個概念在運算子的 B-J 正交性的特徵化中扮演了非常重要的角色。本書研究了 Hilbert 空間運算子的範數達成集的結構，對於 Banach 空間之間的運算子，其結構尚未完全理解。本書探討了地面空間和運算子空間中 B-J 正交性之間的相互關係，並以最廣泛的泛化形式進行了研究。本書進一步探討了近似 B-J 正交性的概念，並在地面空間和運算子空間中研究了其幾何性質。它突出了有界線性運算子的平滑性和 k-平滑性、定義在 Hilbert 空間和 Banach 空間之間的極端收縮和對稱性等重要的幾何性質。

Arpita Mal is an Inspire Faculty Fellow at the Department of Mathematics, Indian Institute of Science, Bengaluru, under the mentorship of Prof. Apoorva Khare. Dr. Mal completed one year of postdoctoral research with SERB National Post-Doctoral fellowship at the same department, under the same mentor. She was also awarded an NBHM postdoctoral fellowship. She completed her Ph.D. at Jadavpur University, Kolkata, under the supervision of Prof. Kallol Paul in 2021. Dr. Mal is Recipient of a Gold Medal for securing the first-class-first position at M.Sc. from Jadavpur University. With 25 research articles in different international journals of high reputation, her research interest includes the geometry of Banach space and operator space.
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.

Arpita Mal是印度科學研究所數學系的Inspire Faculty Fellow，她的導師是Apoorva Khare教授。Mal博士在同一系所以及同一導師的指導下，完成了一年的SERB國家博士後研究。她還獲得了NBHM博士後研究獎學金。她在2021年在Jadavpur大學完成了她的博士學位，指導教授是Kallol Paul教授。Mal博士在Jadavpur大學獲得了一枚金牌，以表彰她在碩士學位中獲得了第一名的成績。她在不同國際高聲譽期刊上發表了25篇研究文章，她的研究興趣包括Banach空間和算子空間的幾何學。

Kallol Paul是印度Jadavpur大學數學系的教授。他在Gauhati大學（阿薩姆邦）獲得數學學士學位，並在Jadavpur大學獲得碩士學位，兩次考試都獲得第一名。他的研究範圍涵蓋了函數分析和算子理論。擁有超過26年的教學和研究經驗，他迄今為止指導了16名學生成功完成博士學位，另外6名學生正在他的指導下進行博士研究。他在各種國際聲譽期刊上發表了超過140篇論文。他目前的教學範圍包括實分析、度量空間和算子理論。目前，他積極參與各種主題的研究，包括數值半徑不等式、Birkhoff-James正交性及其在Banach空間研究中的應用。作為一個擁有廣泛國際合作夥伴網絡的教授，Paul教授在確立Jadavpur大學作為Banach空間理論研究重要中心方面發揮了關鍵作用。

Debmalya Sain是印度信息技術拉伊奇爾分校數學與計算系的助理教授。他畢業於Ramakrishna Mission Vidyapith，Purulia，並在Kallol Paul教授的指導下於2015年獲得博士學位。他在本科和研究生學習中多次獲得金牌，並在Jadavpur大學考試中獲得了第一名。他在Bengaluru的印度科學研究所在Gadadhar Misra教授和Apoorva Khare教授的指導下完成了多個博士後研究。他還獲得了許多國際獎助金和獎項，包括在Miguel Martin教授的指導下在西班牙格拉納達大學進行研究的Maria Zambrano獎學金。Sain博士在各種國際聲譽期刊上發表了75多篇文章。除了擔任許多國際期刊的審稿人和評審外，他還是由Birkhauser出版的《Advances in Operator Theory》期刊的邀請成員。