Strongly Exposed Points of Decomposable Sets in Spaces of Bochner Integrable Functions

Author: Tolstonogov, A.A.

Source: , 1 January 2002, vol. 71, no. 1-1, pp. 267-275(9)

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Abstract:

A characterization of strongly exposed points of a decomposable bounded closed convex set \Gamma\subset L_p(T,X), where 1\le p< \nomathbreak \infty, in terms of strongly exposed points of values of the set-valued representation F\:T\to \nomathbreak 2^X of \Gamma is given. As a corollary, necessary conditions characterizing strongly exposed points of the unit ball in L_p(T,X), where 1\le p< \nomathbreak \infty, in terms of strongly exposed points of the unit ball in X are obtained.

Keywords: Bochner -spaces; convex set; decomposable set; set-valued map; set-valued representation; strongly exposed point

Document Type: Regular Paper

Affiliations: Institute of System Dynamics and Control Theory, Siberian Division, Russian Academy of Sciences aatiol@icc.ru

Publication date: January 1, 2002

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