A First Course in Functional Analysis

ISBN-13: 9781498771610 / Angielski / Twarda / 2017 / 240 str.

Orr Moshe Shalit

Opis

This book is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The main aim is to develop rigorously 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 structured, with an emphasis on clarity and logical development alongside real applications in analysis.

Spis treści

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.

O autorze

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.