On algebras of Banach algebra-valued bounded continuous functions

Let X be a completely regular Hausdorff space. We denote by C (X, A) the algebra of all continuous functions on X with values in a complex commutative unital Banach algebra A. Let C-b (X, A) be its subalgebra consisting of all bounded continuous functions and endowed with the uniform norm. In this paper, we give conditions equivalent to the density of a natural continuous image of X x M (A) in the maximal ideal space of C-b (X, A).