on character space of the algebra of bse-functions

Suppose that a is a semi-simple and commutative banach algebra. in this paper we try to characterize the character space of the banach algebra cbse(δ(a)) consisting of all bse-functions on δ(a) where δ(a) denotes the character space of a. indeed, in the case that a=c0(x) where x is a non-empty locally compact hausdroff space, we give a complete characterization of δ(cbse(δ(a))) and in the general case we give a partial answer. also, using the fourier algebra, we show that cbse(δ(a)) is not a c∗-algebra in general. finally for some subsets e of a∗, we define the subspace of bse-like functions on δ(a)∪e and give a nice application of this space related to goldstine's theorem.