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Journal of the London Mathematical Society 1992 s2-46(3):482-490; doi:10.1112/jlms/s2-46.3.482
© 1992 by London Mathematical Society
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© Oxford University Press

Embeddings of Spaces of Holomorphic Functions of Bounded Type

J. M. Ansemil, R. M. Aron and S. Ponte

Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, Ciudad Universitaria 28040 Madrid, Spain
Department of Mathematics, Kent State University Kent, Ohio 44242, USA

Let U be an open subset of a complex locally convex space E, let F be a closed subspace of E, and let pcy:E/F be the canonical quotient mapping. In this paper we study the induced mapping pcy*, taking f {varepsilon} Hb{pcy(U)) -> fo pcy {varepsilon} Hb, where Hb(V) denotes the space of holomorphic functions of bounded type on an open set V. We prove that this mapping is an embedding when E is a Fréchet-Schwartz space, and that it is not an embedding for certain subspaces F of every Fréchet-Montel, not Schwartz, space. We provide several examples in the case where E is a Banach space to illustrate the sharpness of our results.


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