# $C^*$-algebra books recommendations

The maximal ideal space of a commutative $$C^*$$-algebra is a compact Hausdorff space and it is one way to construct a compactification of a topological space. I am looking for an introductory book in commutative $$C^*$$-algebra that has a treatment of the properties of a topological space in the sense that the book gives properties of a topological space that can be derived from the $$C^*$$-algebra of the continuous bounded complex-valued function on that space and vice versa.

• An older book (1971), my I studied it when I still had access to the university library : Semadeni, Banach spaces of continuous functions (vol 1), not sure if a vol. 2 ever came out. Quite thorough on the basics, in my memory. – Henno Brandsma Apr 7 at 21:25