Kothe spaces modeled on spaces of C-infinity functions

The isomorphic classification problem for the Kothe models of some C-infinity function spaces is considered. By making use of some interpolative neighborhoods which are related to the linear topological invariant D-psi and other invariants related to the ''quantity'' characteristics of the space, it necessary condition for the isomorphism of two such spaces is proved. As applications, it is shown that some pairs of spaces which have the same interpolation property D-phi are not isomorphic.