On non-primary Fréchet Schwartz spaces

Tom 126 / 1997

J. C. Díaz Studia Mathematica 126 (1997), 291-307 DOI: 10.4064/sm-126-3-291-307


Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic functions of bounded type $ℋ_b(U)$, where U is a Banach space or a bounded absolutely convex open set in a Banach space.


  • J. C. Díaz

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