Martingale decomposition of Dirichlet processes on the Banach space C0[0, 1]

We prove that for a given symmetric Dirichlet form of type g(u, v) = [integral operator]E<A(z)[backward difference]u(z), [backward difference]v(z)>h[mu](dz) with E = C0[0, 1] and H = classical Cameron-Martin space the corresponding diffusion process (under P[mu]) can be decomposed into a forward and a backward E-valued martingale. The construction of the martingale is direct and explicit since it is based on a modification of Lévy's construction of Brownian motion. Applications to prove tightness of laws of diffusions of the above kind are given.