A first course in functional analysis

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. Content: Introduction and the Stone-Weierstrass theorem. Hilbert spaces. Orthogonality, projections, and bases. Fourier series. Bounded linear operators on Hilbert space. Hilbert function spaces. Banach spaces. The algebra of bounded operators on a Banach space. Compact operators. Compact operators on Hilbert space. Applications of compact operators. The Fourier transform. *The Hahn-Banach Theorems. Metric and topological spaces.