  We show that a continuous bilinear mapping P: C(I) \times C(I) \to C(I) can
be presented in the form P(f,g) = B((Af)(Ag)), where A and B are bounded linear
operators on C(I) and multiplication is defined pointwise, if and only if for
all t in I the bilinear form (f,g) -> P(f,g)(t) is integral on C(I) times C(I)
and depends in a sense continuously on t. To this end we construct a continuous
surjection phi : I \to I^2 admitting a regular averaging operator in the sense
of Pelczynski.
