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Embeddings of spaces of holomorphic functions of bounded type

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

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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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