Good references(books or lecture notes) for self study on Banach Algebra.

Question

Can someone suggest some good references(books or lecture notes) for self study on Banach Algebra?

By background being a first course in Functional Analysis and a course in Measure Theory.

Most preferably other than some of known to be:

• Rudin, Functional Analysis.

• Conway, Functional Analysis.

Thank You.

Answer 1

I would suggest the book by Richard V. Kadison/John R. Ringrose, Fundamentals of the Theory of Operator Algebras Volume I, and you may pair this one with another book by Corneliu Constantinescu, $C^{\ast}$-algebras Volume II.

These two books assume little background of measure theory, they even do not assume very much about Functional Analysis, so I think they suit for your need.

Answer 2

I can suggest a few good books for this:

• W. Arveson's A short course on Spectral Theory
• R. Douglas' Banach Algebra Techniques in Operator theory
• G. Murphy's C-star algebras and Operator theory