On the "three-space problem" for spaces of polynomials.



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Ansemil, José María M. and Blasco Contreras, Fernando and Ponte, Socorro (1997) On the "three-space problem" for spaces of polynomials. Note di Matematica, 17 . pp. 185-195. ISSN 1123-2536

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Official URL: http://siba-ese.unisalento.it/index.php/notemat/article/view/870/726


A property P of locally convex spaces is called a three-space property whenever the following implication holds: if both a closed subspace F and the corresponding quotient E/F of a locally convex space E have P then E has P as well. The authors consider properties P of the form: E has P whenever two "natural'' topologies coincide on the spaces of n-homogeneous polynomials on E. They consider topologies of the uniform convergence on all absolutely convex compact or bounded subsets as well as the strong topology and the Nachbin ported topology. The results obtained are mostly negative and the counterexamples are variations of the known spaces.

Item Type:Article
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Proceedings of the Second International Workshop on Functional Analysis (Trier, 1997)

Uncontrolled Keywords:Three-space problem; spaces of polynomials
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:22556
Deposited On:24 Jul 2013 11:08
Last Modified:10 Aug 2018 08:55

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