RT Journal Article
T1 Embeddings of spaces of holomorphic functions of bounded type
A1 Martínez Ansemil, José María
A1 Aron, Richard M.
A1 Ponte Miramontes, María Del Socorro
AB Let U be an open subset of a complex locally convex space E, let F be a closed subspace of E, and let PI:E --> E/F be the canonical quotient mapping. In this paper we study the induced mapping PI*, taking f is-an-element-of H(b)(PI(U))--> f circle PI is-an-element-of H(b)(U), where H(b)(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 Frechet-Schwartz space, and that it is not an embedding for certain subspaces F of every Frechet-Montel, not Schwartz, space. We provide several examples in the case where E is a Banach space to illustrate the sharpness of our results.
PB Oxford University Press
SN 0024-6107
YR 1992
FD 1992-12
LK https://hdl.handle.net/20.500.14352/57630
UL https://hdl.handle.net/20.500.14352/57630
DS Docta Complutense
RD 1 sept 2024