Factorization of holomorphic mappings in infinite dimensions (Q1087796)

Let E be a complex locally convex space and let F be a subspace of E. We establish necessary and sufficient conditions for a holomorphic function on E to factor through the quotient space E/F. In the case where E is a Banach space, we examine when certain properties of a factorizable holomorphic function on E are preserved. Consequences of this when \(E=c_ 0\) and \(E=Tsirelson's\) original space are discussed. Finally, we examine the topological nature of the natural inclusion of H(E/F) in H(E).