A Note on Holomorphic Functions of Bounded Type in Fréchet Spaces

If E is a complex Fréchet space, F is an infinite dimensional closed subspace of E such that E/F is not Montel, and Π: E → E/F is the canonical quotient mapping, we prove here that there always is an absolutely convex open set U in E such that the induced mapping Π*: Hb(Π(U)) → Hb(U) is not an embedding. Other related results are given.