Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces

• Autorzy: Seán Dineen
• Języki publikacji: EN

Abstrakty

EN

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 with DN [2, 4, 5, 6] - together with new examples, e.g. Banach spaces with an unconditional finite-dimensional Schauder decomposition and certain Fréchet-Schwartz spaces. This gives the first examples of Fréchet spaces, which are not nuclear, with τ_{0} = τ_{δ} on H(E).

Kategorie tematyczne

• 46G20: Infinite-dimensional holomorphy
• 32A05: Power series, series of functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 113
• Numer: 1
• Strony: 43-54

Daty

wydano

1995

otrzymano

1993-05-19

poprawiono

1994-06-27

Twórcy

autor

Seán Dineen

• Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland

Bibliografia

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