An operator representation for weighted inductive limits of spaces of vector valued holomorphic functions

NW discuss the problem when an isomorphism VH(G, E-b(1)) = L-b(E, VH(G)) holds for woightcd (LB)-spaces VH(G) and Frechet spaces E. There is a close connection to a special case of Grothendieck's "probleme des topologies", which raises the (open) question under which conditions VH(G) has (QNo)' in the terminology of Peris [28]. We also point out an interesting relation to vector valued projective description. In the last section, a result on weighted inductive limits of spaces of holomorphic functions on product sets is given.