The Itô integral and the Hitsuda–Skorohod integral in the infinite dimensional case

The criterion of adaptedness of a Hilbert space valued stochastic process to the filtration generated by a cylindrical Wiener process is obtained in terms of the S-transform. The criterion is then used to establish the connection between the Itô integral with respect to a cylindrical Wiener process and the Hitsuda–Skhorohod integral in the space of Hilbert space valued stochastic distributions.