Geodesic
Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces
Studia Mathematica, Tome 113 (1995) no. 1, pp. 43-54

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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).
DOI : 10.4064/sm-113-1-43-54

Seán Dineen 1

1 
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Seán Dineen. Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces. Studia Mathematica, Tome 113 (1995) no. 1, pp. 43-54. doi: 10.4064/sm-113-1-43-54

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