M. THAMBAN NAIR – HOD, Department of Mathematics at IIT Madras, Chennai

Thamban Nair M 
Office: HSB - 252B, Department of Mathematics, IIT Madras
Research Interests:Applicable Functional Analysis,
Spectral Approximation, Operator Equations, Inverse 
and Ill-posed Problems
Phone:+91 - 44 - 22574601
Fax: +91 - 44 - 22574602
Email: mahead@iitm.ac.in
Departmental web page

Price: Rs. 350.00
ISBN: 978-81-203-1735-2
Pages: 448
Binding: Paper Back
Buy Now at www.phindia.com
Intended as an introductory-level text on Functional Analysis for the postgraduate students in Mathematics, this compact and well-organized text covers all the topics considered essential to the subject. In so doing, it provides a very good understanding of the subject to the reader.
The book begins with a review of linear algebra, and then it goes on to give the basic notion of a norm on linear space (proving thereby most of the basic results), progresses gradually, dealing with operators, and proves some of the basic theorems of Functional Analysis. Besides, the book analyzes more advanced topics like dual space considerations, compact operators, and spectral theory of Banach and Hilbert space operators.
The text is so organized that it strives, particularly in the last chapter, to apply and relate the basic theorems to problems which arise while solving operator equations.
• Plenty of examples have been worked out in detail, which not only illustrate a particular result, but also point towards its limitations so that subsequent stronger results follow.
• Exercises, which are meant to aid understanding and to promote mastery of the subject, are interspersed throughout the text.

This student friendly text, with its clear exposition of concepts, should prove to be a boon to the beginner aspiring to have an insight into Functional Analysis.

Preface. Acknowledgements. Note to the Reader. Review of Linear Algebra. Normed Linear Spaces. Operators on Normed Linear Spaces. More about Hilbert Spaces. Hahn-Banach Theorem and Its Consequences. Uniform Boundedness Principle. Closed Graph Theorem and Its Consequences. Dual Space Consid-erations. Compact Operators. Spectral Results for Banach Space Operators. Operators on Hilbert Spaces. Spectral Results for Hilbert Space Operators. Spectral Representations. Solution of Operator Equations. References. Index.
M. THAMBAN NAIR, Ph.D., Post Doctoral Fellow, University of Grenoble (France), is Head of the Department, Department of Mathematics at Indian Institute of Technology Madras, Chennai. He has held visiting positions at Australian National University, Canberra, and University of Kaiserslautern (Germany) on several occasions. Besides, he has given many invited talks at various institutions in India and abroad.
A vigorous researcher in the area of Numerical Functional Analysis, Dr. Nair has published a number of research papers in reputed national and international journals, including Journal of Indian Mathematical Society, Numerical Functional Analysis and Optimization, Proceedings of American Mathematical Society, Integral Equations and Operator Theory and Studia Mathematica.
2001 / 448pp. / 16.0 x 24.1 cm / ISBN978-81-203-1735-2 / Rs.350.00
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