On complemented subspaces of non-Archimedean Kothe spaces

The generalized power series spaces D-f (a, r) are the most known and important examples of nuclear Kothe spaces. We prove that every Kothe-Montel space (over a non-Archimedean field K) has a complemented closed subspace isomorphic to a generalized power series space D-f (a, r). It follows that every non-normable Frechet space E that is not isomorphic to the product of a Banach space and the space K-N has a closed subspace isomorphic to a generalized power series space D-f (a, r). (C) 2018 Elsevier Inc. All rights reserved.