Weighted Inductive Limits of Holomorphic Functions with o-Growth Condition

摘要

We study topological properties of weighted (LB)-spaces of holomorphic functions on open sets with o-growth condition. We show that such spaces are semi-Montel if and only if they are (DFS). We also establish that, for a wide family of open sets, some important topological properties of such holomorphic spaces are always equivalent and necessary for a space to be equal algebraically to its projective hull. This means, in particular, that for such open sets these spaces behave in a very similar way as the corresponding spaces of continuous functions.