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Spaces of holomorphic functions and germs on quotients

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

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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
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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