ON THE CHARACTER SPACE OF BANACH VECTOR-VALUED FUNCTION ALGEBRAS

Given a compact space X and a commutative Banach algebra A, the character spaces of A-valued function algebras on X are investigated. The class of natural A-valued function algebras, those whose characters can be described by means of characters of A and point evaluation homomorphisms, is introduced and studied. For an admissible Banach A-valued function algebra A on X, conditions under which the character space m(A) is homeomorphic to m(u) x m(A) are presented, where u = C(X) boolean AND A is the subalgebra of A consisting of scalar-valued functions. An illustration of the results is given by some examples.