Proximinal subspaces of A ( K ) of finite codimension

T. S. S. R. K. Rao

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-5

Abstract:

We study an analogue of Garkavi's result on proximinal subspaces of C ( X ) of finite codimension in the context of the space A ( K ) of affine continuous functions on a compact convex set K . We give an example to show that a simple-minded analogue of Garkavi's result fails for these spaces. When K is a metrizable Choquet simplex, we give a necessary and sufficient condition for a boundary measure to attain its norm on A ( K ) . We also exhibit proximinal subspaces of finite codimension of A ( K ) when the measures are supported on a compact subset of the extreme boundary.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:417904

DOI: 10.1155/S0161171203212308

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