Page "Banach algebra" Paragraph 42

1.

Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.

Moreover, the norm ( i. e., operator norm ) of a character is one.

Equipped with the topology of pointwise convergence on A ( i. e., the topology induced by the weak -* topology of A < sup >∗</ sup >), the character space, Δ ( A ), is a Hausdorff compact space.