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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 I (DN) and that Hb(E*) I (?) when E I (?) 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 I (DN) n (?) is stablished when J(V) is finitely generated by continuous polynomials on E*.

Linear topological invariants of spaces of holomorphic functions in infinite dimension