Publication:
Embeddings of spaces of holomorphic functions of bounded type

dc.contributor.authorAnsemil, José María M.
dc.contributor.authorAron, Richard M.
dc.contributor.authorPonte, Socorro
dc.date.accessioned2023-06-20T17:01:01Z
dc.date.available2023-06-20T17:01:01Z
dc.date.issued1992-12
dc.description.abstractLet 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.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/16817
dc.identifier.issn0024-6107
dc.identifier.officialurlhttp://jlms.oxfordjournals.org/content/s2-46/3/482.full.pdf+html
dc.identifier.relatedurlhttp://www.oxfordjournals.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57630
dc.issue.number3
dc.journal.titleJournal of the London Mathematical Society. Second Series
dc.page.final490
dc.page.initial482
dc.publisherOxford University Press
dc.rights.accessRightsmetadata only access
dc.subject.cdu515.12
dc.subject.keywordspace of holomorphic functions of bounded type on an open set
dc.subject.keywordembedding
dc.subject.keywordFréchet-Schwartz space
dc.subject.ucmTopología
dc.subject.unesco1210 Topología
dc.titleEmbeddings of spaces of holomorphic functions of bounded type
dc.typejournal article
dc.volume.number46
dspace.entity.typePublication
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