### Impacto

Ansemil, José María M. and Aron, Richard M. and Ponte, Socorro
(1992)
*Spaces of holomorphic functions and germs on quotients.*
In
Progress in Functional Analysis.
North-Holland mathematics studies
(170).
Elsevier Science Publ. B. V., Amsterdam, pp. 163-177.
ISBN 0-444-89378-4

Official URL: http://www.sciencedirect.com/science/article/pii/S0304020808703177

## Abstract

Let E be a complex locally convex space, F a closed subspace, and let π be the canonical quotient mapping from E onto E/F. Let H(U) [resp. H(K)] be the set of holomorphic functions on the open set U of E [resp. the set of germs of holomorphic functions on the compact set K of E]. Let π∗ be the mapping induced by π from H(π(U)) [resp. H(π(K))] into H(U) [resp. H(K)].

π∗ is always continuous for the natural topologies; the aim of the paper is to give a survey of the results concerning when π∗ is, or is not, an embedding.

Item Type: | Book Section |
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Additional Information: | INTERNATIONAL FUNCTIONAL ANALYSIS MEETING ON THE OCCASION OF THE 60TH BIRTHDAY OF PROFESSOR M VALDIVIA.PENISCOLA,OCT 22-27, 1990 |

Uncontrolled Keywords: | holomorphic mappings on quotient spaces; compact open topology; embedding; Fréchet-Montel non-Schwartz space; Montel space |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 16818 |

Deposited On: | 23 Oct 2012 08:19 |

Last Modified: | 10 Dec 2013 17:44 |

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