Elements Of Functional Analysis And Operator Theory

The book aims not only to present the core concepts in a clear and concise manner, but also to enrich the reader's understanding through numerous illustrations and a wide range of exercise problems. Special focus has been laid on important theorems like open map theorem, closed graph theorem, Hahn-Banach theorems, principle of uniform boundedness, etc, which play a crucial role in the study of functional analysis. Moreover, the reader will also find brief discussions on various tricky topics like comparison between two types of adjoint operators — Hilbert space adjoint and Banach space adjoint, etc. Careful attention has been paid on the hypothesis of the results and counterexamples have been provided for their significance.

The prerequisites for this book include undergraduate courses in real analysis, linear algebra and basic point set topology (for example, metric spaces). Beyond this, some familiarity with measure theory and Lebesgue integration is desirable, but not essential. Most of the use of measure theory and Lebesgue integration occurs in limited ways.

In 1989, Subiman Kundu completed his PhD on function spaces at Virginia Tech., USA under the supervision of Prof. Robert A McCoy. For more than three decades, he served at Department of Mathematics, Indian Institute of Technology Delhi, India. In 2022, he retired as a professor of Mathematics from the same department. In addition to research, he enjoyed teaching pretty much. At present, he is engaged in writing several books. One of his research monographs (in collaboration with M Aggarwal and L Gupta) and a textbook (in collaboration with M Aggarwal) are published by World Scientific.

Manisha Aggarwal completed her PhD in Mathematics at Indian Institute of Technology Delhi, India in 2016 under the supervision of Prof. Subiman Kundu. She taught various courses at St. Stephen's College, University of Delhi, India for more than eight years. In 2024, she joined Department of Mathematical and Computational Sciences in National Institute of Technology Karnataka. Her passion for teaching and research has motivated her to write textbooks for undergraduates and postgraduates in collaboration with Prof. Kundu.