Shalit O.M. A First Course in Functional Analysis

Taylor & Francis Group, LLC, 2017. — 257 p. — ISBN: 1498771610Written 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.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 the theory of compact operators
The Fourier transform
The Hahn-Banach theorems
Metric and topological spaces