ON NONPRIMARY SCHWARTZ,FRECHET SPACES

Let E be a Frechet Schwartz space with a continuous norm and with a fi nite-dimensional decomposition, and let F be any finite-dimensional su bspace of E. It is proved that E can be written as G+H where G and H d o not contain any subspace isomorphic to F. In particular, E is not pr imary. If the subspace F is not normable then the statement holds for other quasinormable Frechet spaces, e.g., if E is a quasinormable and locally normable Kothe sequence space, or if E is a space of holomorph ic functions of bounded type H-b(U), where U is a Banach space or a bo unded absolutely convex open set in a Banach space.