Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces

Volume 101 / 1991

Manfred Scheve Studia Mathematica 101 (1991), 83-104 DOI: 10.4064/sm-101-1-83-104


Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from the theory of linear operators between Fréchet spaces.


  • Manfred Scheve

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