An Introduction to Operators on the Hardy-Hilbert Space

Rubén A. Martínez-Avendaño, Peter Rosenthal (auth.)9780387354187, 9780387485782, 0387354182, 0387485783

The subject of this book is operator theory on the Hardy space H2, also called the Hardy-Hilbert space. This is a popular area, partially because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters the material covered in this book will have acquired a firm foundation for the study of all spaces of analytic functions and of operators on them. The goal is to provide an elementary and engaging introduction to this subject that will be readable by everyone who has understood introductory courses in complex analysis and in functional analysis. The exposition, blending techniques from “soft” and “hard” analysis, is intended to be as clear and instructive as possible. Many of the proofs are very elegant.

This book evolved from a graduate course that was taught at the University of Toronto. It should prove suitable as a textbook for beginning graduate students, or even for well-prepared advanced undergraduates, as well as for independent study. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.

Table of contents :
Front Matter….Pages i-xii
Introduction….Pages 1-35
The Unilateral Shift and Factorization of Functions….Pages 37-94
Toeplitz Operators….Pages 95-121
Hankel Operators….Pages 123-162
Composition Operators….Pages 163-195
Further Reading….Pages 197-199
Back Matter….Pages 201-223