On non-primary Fréchet Schwartz spaces

Díaz, J.

Díaz, J.

Studia Mathematica, Tome 122 (1997), p. 291-307 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 1997-01-01

Zbl 0896.46001

EUDML-ID : urn:eudml:doc:216456

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     title = {On non-primary Fr\'echet Schwartz spaces},
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     volume = {122},
     year = {1997},
     pages = {291-307},
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Díaz, J. On non-primary Fréchet Schwartz spaces. Studia Mathematica, Tome 122 (1997) pp. 291-307. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv126i3p291bwm/

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