2024-02-25T09:36:37Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/576302023-06-23T12:30:36Zcom_20.500.14352_14col_20.500.14352_15
Embeddings of spaces of holomorphic functions of bounded type
Ansemil, José María M.
Aron, Richard M.
Ponte, Socorro
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.
2023-06-20T17:01:01Z
2023-06-20T17:01:01Z
2023-06-20T17:01:01Z
1992-12
journal article
https://hdl.handle.net/20.500.14352/57630
0024-6107
http://jlms.oxfordjournals.org/content/s2-46/3/482.full.pdf+html
http://www.oxfordjournals.org/
metadata only access
Oxford University Press