Espaces localement convexes séparés différentiables.

Gjinushi, Skender (1978) Espaces localement convexes séparés différentiables. Initiation à l'analyse, 11 (11). pp. 1-14.

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In the context of Banach spaces, we now have a collection of beautiful results relating the Radon-Nikodým and the differentiability properties to the existence of denting, extreme and strongly exposed points. The present note is a report (without proof) on the author's investigation of the problem of extending the Banach space results to larger classes of locally convex spaces. In order to give the flavor of the results we cite one: Let E be a barrelled locally convex space such that each bounded closed subset is complete, metrizable and dentable and such that the dual space is Fréchet. Then each bounded closed convex subset of E is the closed convex hull of its strongly exposed points. In case E is a Banach space, this theorem is due to R. R. Phelps [J. Functional Analysis 17 (1974), 78–90; MR0352941].

Item Type: Article
Subjects: Q Science >
Divisions: Engineering, Science and Mathematics > Mathematics
Depositing User: Editor Risat
Date Deposited: 31 Mar 2018 20:02
Last Modified: 08 May 2018 08:00

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