It is shown that if E is a Frechet space with the strong dual E* then Hb(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 Hb(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 when J(V) is finitely generated by continuous polynomials on E*.
@article{urn:eudml:doc:41220,
title = {Linear topological invariants of spaces of holomorphic functions in infinite dimension.},
journal = {Publicacions Matem\`atiques},
volume = {39},
year = {1995},
pages = {71-88},
mrnumber = {MR1336357},
zbl = {0836.46026},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41220}
}
Minh Ha, Nguyen; Hai, Le Mau. Linear topological invariants of spaces of holomorphic functions in infinite dimension.. Publicacions Matemàtiques, Tome 39 (1995) pp. 71-88. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41220/