Functional Analysis (Paperback)

Functional Analysis Book Description

This book is an introductory text written with minimal prerequisites. The plan is to impose a distance structure on a linear space, exploit it fully and then introduce additional features only when one cannot get any further without them. The book naturally falls into two parts and each of them is developed independently of the other The first part deals with normed spaces, their completeness and continuous linear maps on them, including the theory of compact operators. The much shorter second part treats Hilbert spaces and leads upto the spectral theorem for compact self-adjoint operators. Four appendices point out areas of further development.
Emphasis is on giving a number of examples to illustrate abstract concepts and on citing varirous applications of results proved in the text. In addition to proving existence and uniqueness of a solution, its apprroximate construction is indicated. Problems of varying degrees of difficulty are given at the end of each section. Their statements contain the answers as well.
About the Author(s):
Balmohan V Limaye
The author is Professor of Mathematics at the Indian Institute of Technology Bombay. After completing his doctorate at the University of Rochester, New York, he taught at the University of California. Irvine. He was a member of the School of Mathematics in the Tata Institute of Fundamental Research, Bombay. Dr. Limaye has published numerous research articles in the areas of algebraic analysis and numerical functional analysis. He is a coauthor of A Textbook of Mathematical Analysis and of Real Function Algebras. He has also written a research monograph entitled Spectral Perturbation and Approximation with Numerical Experiments.
Contents:
Preliminaries
Fundamentals of Normed Linear Spaces
Bounded Linear Maps on Banach Spaces
Spaces of Bounded Linear Functionals
Compact Operators on Normed Spaces
Geometry of Hilbert Spaces
Bounded Operators on Hilbert Space
Appendix.

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