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.

chapter Chapter 2|15 pages

Hilbert spaces

chapter Chapter 3|15 pages

Orthogonality, projections, and bases

chapter Chapter 4|17 pages

Fourier series

chapter Chapter 5|21 pages

Bounded linear operators on Hilbert space

chapter Chapter 6|20 pages

Hilbert function spaces

chapter Chapter 7|15 pages

Banach spaces

chapter Chapter 9|8 pages

Compact operators

chapter Chapter 10|15 pages

Compact operators on Hilbert space

chapter Chapter 12|24 pages

The Fourier transform

chapter Chapter 13|15 pages

*The Hahn-Banach theorems