ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46E10/40, 46A04/13/32 Bierstedt, Klaus D. and Holtmanns, Silke, Univ. Paderborn, Germany An operator representation for weighted inductive limits of spaces of vector valued holomorphic functions Starting from the operator representation HV (G, E′_{b}) = L(E, HV (G)) for weighted spaces of vector valued holomorphic functions (cf. the talk by the second-named author), we discuss the rather different question when a topological isomorphism

VH(G, E′_{b}) = L_{b}(E, VH(G))

holds for weighted (LB)-spaces VH(G) and Fréchet spaces E. We point out the relation to a special case of Grothendieck’s “problème des topologies”, which raises the (open) question under which conditions VH(G) has (QNo)’ in the notation of A. Peris. Moreover, there is an interesting relation to the vector valued projective description problem. (The talk will be given by the first-named author.)