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Ansemil, José María M. and Aron, Richard M. and Ponte, Socorro
(1992)
*Embeddings of spaces of holomorphic functions of bounded type.*
Journal of the London Mathematical Society. Second Series, 46
(3).
pp. 482-490.
ISSN 0024-6107

Official URL: http://jlms.oxfordjournals.org/content/s2-46/3/482.full.pdf+html

## Abstract

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.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | space of holomorphic functions of bounded type on an open set; embedding; Fréchet-Schwartz space |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 16817 |

Deposited On: | 23 Oct 2012 08:20 |

Last Modified: | 09 Dec 2013 17:45 |

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