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.
Biography
Orr Moshe Shalit is an assistant professor of mathematics at the Technion - Israel Institute of Technology in Haifa, Israel. His research interests lie in the topic of operator theory and operator algebras. He is the author of over 20 research papers and is a regular reviewer for many prestigious journals.
A First Course in Functional Analysis by Orr Moshe Shalit is an excellent introduction to linear analysis. Its straightforward approach to the key ideas of the field, with special emphasis on Hilbert spaces, will be very much appreciated both by students and instructors. The book is suitable for advanced undergraduates and beginning graduate students who have had prior exposure to advanced calculus and linear algebra. I highly recommend this book to anyone teaching a first course in abstract analysis.
—Jens Harlander, Boise State University
