On the character space of Banach vector-valued function algebras

ýGiven a compact space X and a commutative Banach algebraý ýAý, ýthe character spaces of A-valued function algebras on X areý ýinvestigatedý. ýThe class of natural A-valued function algebrasý, ýthose whose characters can be described by means of characters of A andý ýpoint evaluation homomorphismsý, ýis introduced and studiedý. ýFor aný ýadmissible Banach A-valued function algebra A on Xý, ýconditions under which the character space M(A)ý ýis homeomorphic to M(A)×M(A) are presentedý, ýwhere A=C(X)∩Aý ýis the subalgebra of A consisting of scalar-valued functionsý. ýAn illustration of the results is given by some examples.