Suppose X and Y are
topological vector spaces. This paper gives an analytic representation of continuous
linear operators from C into Y , where C denotes the space of continuous functions
from the interval [0,1] into X with the topology of uniform convergence. In order
to obtain an integral representation theorem analogous to the ones given
by R. K. Goodrich for the locally convex setting in Trans. Amer. Math.
Soc. 131 (1968), 246-258, certain strong hypotheses on C must be assumed
because of the need to be able to extend the operators to a subset of the
double dual of C. However, by using the notion of v-integral, it is possible to
avoid this problem and give a representation theorem without additional
hypothesis.
