Quasi-Normable Preduals of Spaces of Holomorphic Functions

Abstract Let H ( U ) denote the space of all holomorphic functions on an open subset U of a separable Frechet space E . Let τ ω 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 ), τ ω ) satisfies the strict Mackey convergence condition.