References for Banach Space Theory

Question

Currently I am investigating the proof of Banach-Stone Theorem.. I would like to strengthen my background in Banach Spaces so that I can fully understand the proof. I am using this to study the proof. Are there any recommended books for Banach Spaces theory? I come across the book 'Banach Space Theory: The Basis for Linear and Nonlinear Analysis'. It seems quite a good book to me.

Answer 1

For the first reading I recommend first 3 chapters of Banach space theory. The basis for linear and non-linear analysis. M. Fabian, P. Habala, P. Hajek, V. Montesinos, V. Zizler

Then you can move to very basic standard i.e. to Topics in Banach space theory. F. Albiac, N. Kalton. And after that return to the first textbook.

If you are interested precisely in isometries between Banach spaces, then I also recommend The isometric theory of classical Banach spaces. H. E. Lacey. It contains more advanced parts of Banach space theory.