Displaying similar documents to “R-Schauder decompositions. Some applications.”

On non-primary Fréchet Schwartz spaces

J. Díaz (1997)

Studia Mathematica

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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...

Preduals of spaces of vector-valued holomorphic functions

Christopher Boyd (2003)

Czechoslovak Mathematical Journal

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For U a balanced open subset of a Fréchet space E and F a dual-Banach space we introduce the topology τ γ on the space ℋ ( U , F ) of holomorphic functions from U into F . This topology allows us to construct a predual for ( ℋ ( U , F ) , τ δ ) which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic...

Holomorphic functions on strict inductive limits of Banach spaces.

Seán Dineen, Luiza A. Moraes (1992)

Revista Matemática de la Universidad Complutense de Madrid

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In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.