Weighted Inductive Limits of Holomorphic Functions with o-Growth Condition
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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.
KeywordsWeighted function spaces Weighted inductive limits Growth conditions
Mathematics Subject ClassificationPrimary 46E10 30H05 46A13
This note was written when the second author visited the Department of Applied Mathematics at the University of Washington. He would like to thank the Department and Professor Aleksandr Aravkin for the hospitality.
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