Ebook: A Short Course on Spectral Theory
Author: William Arveson (auth.)
- Genre: Mathematics // Analysis
- Tags: Analysis, Operator Theory, Functional Analysis
- Series: Graduate Texts in Mathematics 209
- Year: 2002
- Publisher: Springer-Verlag New York
- City: New York
- Edition: 1
- Language: English
- pdf
This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative k-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here. The book is based on a fifteen-week course which the author offered to first or second year graduate students with a foundation in measure theory and elementary functional analysis.
You can find the same material in a bunch of books... but the exposition by Arveson is really superb. He actually EXPLAINS things, not just a list of theorems and proofs with no apparent reason.
The book is 130p only, so it might be ideal for self study. Not everything is in the text but if you want to try the exercises (you might need further reading to do some of them) and you do the extra reading from other sources, you will end up getting a good understanding.
The chapters are: 1. Spectral theory and Banach algebras, 2. Operators on Hilbert space, 3. Asymptotics: Compact perturbations and Fredholm theory and 4. Methods and applications
approximatelly 170 exercises.
The most inspiring book on the subject I have seen, up to now.