# On non-primary Fréchet Schwartz spaces

Studia Mathematica (1997)

- Volume: 126, Issue: 3, page 291-307
- ISSN: 0039-3223

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topDíaz, J.. "On non-primary Fréchet Schwartz spaces." Studia Mathematica 126.3 (1997): 291-307. <http://eudml.org/doc/216456>.

@article{Díaz1997,

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.},

author = {Díaz, J.},

journal = {Studia Mathematica},

keywords = {Fréchet spaces; primary spaces; Schwartz spaces; unconditional decompositions; spaces of Moscatelli type; holomorphic functions of bounded type; Fréchet Schwartz space; continuous norm; finite-dimensional decomposition; quasinormable Fréchet spaces; locally normable Köthe sequence space; space of holomorphic functions of bounded type; bounded absolutely convex open set},

language = {eng},

number = {3},

pages = {291-307},

title = {On non-primary Fréchet Schwartz spaces},

url = {http://eudml.org/doc/216456},

volume = {126},

year = {1997},

}

TY - JOUR

AU - Díaz, J.

TI - On non-primary Fréchet Schwartz spaces

JO - Studia Mathematica

PY - 1997

VL - 126

IS - 3

SP - 291

EP - 307

AB - 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.

LA - eng

KW - Fréchet spaces; primary spaces; Schwartz spaces; unconditional decompositions; spaces of Moscatelli type; holomorphic functions of bounded type; Fréchet Schwartz space; continuous norm; finite-dimensional decomposition; quasinormable Fréchet spaces; locally normable Köthe sequence space; space of holomorphic functions of bounded type; bounded absolutely convex open set

UR - http://eudml.org/doc/216456

ER -

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