# Spectral Theory of Operators on Hilbert Spaces

• Carlos S. Kubrusly
Textbook

1. Front Matter
Pages i-x
2. Carlos S. Kubrusly
Pages 1-25
3. Carlos S. Kubrusly
Pages 27-53
4. Carlos S. Kubrusly
Pages 55-89
5. Carlos S. Kubrusly
Pages 91-129
6. Carlos S. Kubrusly
Pages 131-186
7. Back Matter
Pages 187-197

### Introduction

This work is intended to provide a concise introduction to the spectral theory of Hilbert space operators. With an emphasis on detailed proofs and recent aspects of theory, it can serve as a modern textbook for a first graduate course in the subject. The coverage of topics is thorough, exploring various intricate points and hidden features often left untreated.

The book begins with a primer on Hilbert space theory, summarizing the basics required for the remainder of the book and establishing unified notation and terminology. After this, standard spectral results for (bounded linear) operators on Banach and Hilbert spaces, including the classical partition of the spectrum and spectral properties for specific classes of operators, are discussed. A study of the spectral theorem for normal operators follows, covering both the compact and the general case, and proving both versions of the theorem in full detail. This leads into an investigation of functional calculus for normal operators and Riesz functional calculus, which in turn is followed by Fredholm theory and compact perturbations of the spectrum, where a finer analysis of the spectrum is worked out. Here, further partitions involving the essential spectrum, including the Weyl and Browder spectra, are introduced. The final section of the book deals with Weyl's and Browder's theorems and provides a look at very recent results.

Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will be useful for working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to harness the applications of this theory.

### Keywords

Hilbert space analytic (Riesz) functional calculus functional calculus for normal operators operator theory spectral analysis spectral theorem

#### Authors and affiliations

• Carlos S. Kubrusly
• 1
1. 1., Electrical Engineering DepartmentCatholic University of Rio de JaneiroRio de JaneiroBrazil