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.


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.

  • $\begingroup$ I second the Kadison / Ringrose. I'd also recommend John B Conway's "A Course in Functional Analysis" $\endgroup$ – Moriarty Jan 9 '18 at 4:22

I can suggest a few good books for this:

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

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