Multiplicative functionals on function Algebras

Abstract

ABSTRACT. Leí X be a completely regular Hausdorff space and C(X) the algebra of alí continuous <-valued functions on X ([4] can be found conditions on A under whicls cadi character of A, i.e., each non-zero 1K-linear multiplicative funclional 4xA-* 1K, is given by a point evaluation al sorne point of X.In ibis paper we presení a «Michael» type theorem for the particular case in which X is a real Banach space. As consequence it is showed thai if E is a separable Banach space or E is the topological dual space of a separable Banach space aud A ís the algebra of ah real analytic or the algebra of alí real Cm.functions, ni = 0, 1 oD, on E, then every character 4 of A is a point evaluation at sorne poiní of E.