Spaces of holomorphic functions and germs on quotients
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1992
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Elsevier Science Publ. B. V.
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Martínez Ansemil, J. M., Aron, R. M. & Ponte Miramontes, M. S. «Spaces of Holomorphic Functions and Germs on Quotients». North-Holland Mathematics Studies, vol. 170, Elsevier, 1992, pp. 163-77. DOI.org (Crossref), https://doi.org/10.1016/S0304-0208(08)70317-7.
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.
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INTERNATIONAL FUNCTIONAL ANALYSIS MEETING ON THE OCCASION OF THE 60TH BIRTHDAY OF PROFESSOR M VALDIVIA.PENISCOLA,OCT 22-27, 1990