  Let X be a compact Hausdorf space, let A be a commutative unital Banach
algebra, and let C(X,A) denote the algebra of continuous A-valued functions on
$X$ equipped with the uniform norm ||f||=sup{||f(x)||:x\in X} for all f in
C(X,A). Hausner, in [Proc. Amer. Math. Soc. 8(1957), 246--249], proved that M
is a maximal ideal in C(X,A) if and only if there exist a point x in X and a
maximal ideal N in A such that M={f in C(X,A) : f(x) in N}. In this note, we
give new characterizations of maximal ideals in C(X,A). We also present a short
proof of Hausner's result by a different approach.

Functional Analysis