Quasi-normable preduals of spaces of holomorphic functions

[摘要] Let H(U) denote the space of all holomorphic functions on an open subset U of a separable Frechet space E. Let tau(omega) denote the compact-ported topology on H(U) introduced by Nachbin. Let G(U) denote the predual of H(U) constructed by Mazet. In our main result we show that E is quasi-normable if and only if G(U) is quasi-normable if and only if (H(U), tau(omega)) satisfies the strict Mackey convergence condition. (C) 1997 Academic Press.

[发布日期] 1997-04-01