Full paper in PDF:
$% J. Gómez and J. L. G. Llavona, Multiplicative functionals on function algebras,
Rev. Mat. Univ. Complut. Madrid 1 (1988), no. 1, 2, 3, 19–22.%$
Multiplicative Functionals on Function Algebras
Let
be a completely regular Hausdorff space and
the algebra of
all continuous
-valued functions on
(
or
). If
is
a subalgebra, in Michael (1952) can be found conditions on
under which
each character of 
, i.e., each non-zero
-linear multiplicative functional
, is given by a point evaluation at some point of
.
In this paper we present a “Michael” type theorem for the particular case in
which
is a real Banach space. As a consequence it is showed that if
is a separable Banach space or
is the topological dual space of a separable
Banach space and
is the algebra of all real analytic or the algebra of all real
-functions,
, on
, then every character
of
is a
point evaluation at some point of
.
1980 Mathematics Subject Classification (1985 revision): 46B25.