"The word "spectrum" comes from quantum theory, as does the subject of operators in Hilbert space. Since the early days, the subject has grown, and branched out in a variety of directions. This fact has perhaps made it difficult for an instructor to chose a book from which to teach the fundamental ideas;-- those ideas in a subject that stay constant, even when the fashions change. The topics covered in Arveson's book are relevant now, and are likely to be useful decades from now. They are beautifully presented.-- The material and the format have been tested in courses;-- and this book represents a formula that works!"
"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." |