Displaying similar documents to “Holomorphic functions on Fréchet spaces with Schauder basis.”

Spaces of holomorphic mappings on Banach spaces with a Schauder basis

Jorge Mujica (1997)

Studia Mathematica

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We show that if U is a balanced open subset of a separable Banach space with the bounded approximation property, then the space ℋ(U) of all holomorphic functions on U, with the Nachbin compact-ported topology, is always bornological.

Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces

Seán Dineen (1995)

Studia Mathematica

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We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces...

Weighted spaces of holomorphic functions on Banach spaces

D. García, M. Maestre, P. Rueda (2000)

Studia Mathematica

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We deal with weighted spaces H V 0 ( U ) and HV(U) of holomorphic functions defined on a balanced open subset U of a Banach space X. We give conditions on the weights to ensure that the weighted spaces of m-homogeneous polynomials constitute a Schauder decomposition for them. As an application, we study their reflexivity. We also study the existence of a predual. Several examples are provided.

Analytic functions on c.

Richard M. Aron, Josip Globevnik (1989)

Revista Matemática de la Universidad Complutense de Madrid

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Quasinormability of some spaces of holomorphic mappings.

José M. Isidro (1990)

Revista Matemática de la Universidad Complutense de Madrid

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A class of locally convex vector spaces with a special Schauder decomposition is considered. It is proved that the elements of this class, which includes some spaces naturally appearing in infinite dimensional holomorphy, are quasinormable though in general they are neither metrizable nor Schwartz spaces.