1. Some Basic Concepts in Functional Analysis. 2. Linear Transformations, Linear Functionals and Convexity. 3. Hahn-Banach Theorem. 4. Reflexivity. 5. Banach-Steinhaus Theorem. 6. Closed Graph Theorem and Open Mapping Theorem. 7. Hilbert Spaces. 8. Silverman-Toeplitz Theorem and Schur’s Theorem. 9. Steinhaus Type Theorem.
Biography
P.N. Natarajan (Pinnangudi Narayanasubramanian Natarajan) is former professor and Head, Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai. He got Ph.D. in Analysis from the University of Madras in 1980. An active researcher till date, Prof. Natarajan has over 120 research papers to his credit, published in reputed journals like Proceedings of the American Mathematical Society, Journal of the London Mathematical Society, Indagationes Mathematicae, Annales Mathematiques Blaise Pascal, Commentationes Mathematicae (Prace Matematyczne), p-adic Numbers, Ultrametric Analysis and Applications and Journal of the Indian Mathematical Society. He has so far authored 5 books, published by Springer-Verlag, John Wiley and Taylor and Francis. He has also contributed a chapter each to 3 edited volumes, brought out by Springer-Verlag, Birkhauser-Verlag and Taylor and Francis. His research interests include Summability Theory and Functional Analysis, both Classical and Ultrametric. Prof. Natarajan was honoured with the Dr. Radhakrishnan Award for the Best Teacher in Mathematics for the 1990-1991 by the Government of Tamil Nadu. Besides visiting several institutes of repute in Canada, France, Holland and Greece on invitation, Prof. Natarajan has taken part in several International Conferences and has chaired sessions.
