Operator Theory References and Topics

Question

I wish to do a reading course in Operator Theory. Thus, I am looking for some references in the area. Right now, I have the following two sources available:

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1. Unbounded Self-Adjoint Operators on Hilbert Spaces - Konrad Schumdgen.
2. A course in Operator Theory - J.B. Conway.
3. Linear Operators on Hilbert Spaces - J. Wiedmann.

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Could someone please provide me more references?

Moreover, are there some standard topics that I would do well to cover?

Answer 1

Two popular books are :

1. Douglas' "Banach algebra techniques in Operator Theory" and
2. Murphy's "C* Algebras and Operator theory"

I like Douglas' style, but content-wise, I think Murphy is more standard.

Operator theory and Operator Algebras have a large overlap (particularly at the early-graduate-school level), so any book that professes to teach Operator Algebras would work just as well.

Answer 2

I strongly feel

http://moothathu.files.wordpress.com/2013/03/tksm-operatortheory1.pdf

http://moothathu.files.wordpress.com/2013/03/tksm-operatortheory2.pdf

http://moothathu.files.wordpress.com/2013/03/tksm-operatortheory3.pdf

these would help you.

These are actually lecture notes form a M.Sc course in University of Hyderabad (taught by Dr.T.K.S.Moothathu). He has covered some advanced topics also.. I took his course but dont ask me anything... :P

all the best..