Counterexamples in Holomorphic Functions on Nuclear Fréchet Spaces.
Dietmar Vogt, Reinhold Meise (1983)
Mathematische Zeitschrift
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Counterexamples in Holomorphic Functions on Nuclear Fréchet Spaces.
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(LB)-structure of spaces of germs of holomorphic functions.
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We study the structure of spaces of germs of holomorphic functions on compact sets in Fréchet spaces for (LB) as well as for (Ω,Ω).
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Linear topological invariants of spaces of holomorphic functions in infinite dimension.
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It is shown that if E is a Frechet space with the strong dual E* then H(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that H(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished...