Decompositions of Montel Köthe sequence spaces

Abstract

The following result has been recently proved by the author: Let E be a Fréchet Schwartz space with unconditional basis and with continuous norm; let F be any infinite dimensional subspace of E. Then we can write E as $G⨂ H$ where G and H do not have any subspace isomorphic to F. This theorem is extended here in two directions: (i)If E is a Montel Köthe sequence space (with certain additional assumptions which are satisfied by the examples described in the literature) and the subspace F is Montel non-Schwartz; (ii) If E is any Fréchet Schwartz space with unconditional basis (so the existence of continuous norm is dropped) and F is not isomorphic to $ω$.