This book presents a detailed account of some results about subalgebras of C(X), which carry a Banach algebra norm. It is intended for students who have had a standard graduate real-variable course and be acquainted with a few odds and ends of functional analysis and complex-variables.
1. Bishop’s Stone—Weierstrass Theorem 2. Restriction Algebras Determining C(X) 3. Wermer’s Theorem on Algebras with Multiplicativelt Closed Real Part 4. The Work of Alain Bernard 5. The Theorems of Gorin and Cirka 6. Bounded Approximate Normality, the Work of Bade and Curtis 7. Katznelson’s Bounded Idempotent Theorem 8. Characterization of C(x) by Functions Which Operate
