The density condition in subspaces and quotients of Frechet spaces |
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Authors: | José Bonet Juan Carlos Díaz |
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Institution: | (1) Departamento de Matemática Aplicada E.T.S. Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain;(2) Departamento de Matemática Aplicada, E.T.S.I. Agrónomos, E-14004 Córdoba, Spain |
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Abstract: | The aim of this note is to investigate the topological structure (in particular the density condition) of subspaces and separated quotients of Fréchet spaces. Our main result is the following one: LetE be a Fréchet space which is neither Montel nor isomorphic to a closed subspace ofX × , withX a Banach space, also assume thatE can be written asF G withF andG infinite dimensional closed subspaces ofE not isomorphic to , thenE contains a closed subspace with basis and not satisfying the density condition. We also prove that every Köthe 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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Keywords: | 46A04 46A45 |
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