On non-primary Fréchet Schwartz spaces

J. C.  Díaz

ArticleOriginal scientific text

Title

On non-primary Fréchet Schwartz spaces

Authors ¹

Affiliations

Departamento de Matemáticas, E.T.S.I.A.M., Universidad de Córdoba, 14004 Córdoba, Spain

Abstract

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.

Keywords

ENG

Fréchet spaces, primary spaces, Schwartz spaces, unconditional decompositions, spaces of Moscatelli type, holomorphic functions of bounded type

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Title

On non-primary Fréchet Schwartz spaces

Affiliations

Abstract

Keywords

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