An operator representation for weighted spaces of vector valued holomorphic functions

For any weighted space HV(G) of holomorphic functions on an open set G ⊂ ₵Nwith a topology stronger than that of uniform convergence on the compact sets and for any quasibarrelled space E we prove the topological isomorphism HV(G,E1 b)=Lb(E,HV(G))and derive a similar, more complicated isomorphism for weighted spaces of continuous functions. This generalizes results of [3], [7] and [6] and should be compared with the ∈-product representations for the corresponding spaces of functions with o-growth conditions. At the end we also show the topological isomorphism HV1(G1, HV2(G2)) = H (V1 ⊗ V2)(G1 × G2). © 1999, Birkhäuser Verlag, Basel.