A First Course in Functional Analysis 1st Edition by Orr Moshe Shalit 1498771610 9781498771610

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Product details:

ISBN 10: 1498771610 

ISBN 13: 9781498771610

Author: Orr Moshe Shalit

Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.

Table of contents:

1. Introduction and the Stone-Weierstrass theorem

2. Hilbert spaces

3. Orthogonality, projections, and bases

4. Fourier series

5. Bounded linear operators on Hilbert space

6. Hilbert function spaces

7. Banach spaces

8. The algebra of bounded operators on a Banach space

9. Compact operators

10. Compact operators on Hilbert space

11. Applications of the theory of compact operators

12. The Fourier transform

13. *The Hahn-Banach theorems

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Tags: Orr Moshe Shalit, Course, Functional, Analysis