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Buy Functional Analysis: A First Course

Functional Analysis: A First Course


M. Thamban Nair

Publisher: Phi Learning (2009)
Rs. 250
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Book Summary of Functional Analysis: A First Course

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.

Table of Contents
  • 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 Considerations
  • 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

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