Abstract
The aim of this note is to investigate the topological structure (in particular the density condition) of subspaces and separated quotients of Frechet spaces. Our main result is the following one: LetE be a Frechet space which is neither Montel nor isomorphic to a closed subspace ofX × e, withX a Banach space, also assume thatE can be written asF⊕G withF andG infinite dimensional closed subspaces ofE not isomorphic to e, thenE contains a closed subspace with basis and not satisfying the density condition. We also prove that every Kothe echelon space of orderp, 1<p<∞, which is not quasinormable has a separated quotient with basis which does not satisfy the density condition.
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