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Proximinal subspaces of A ( K ) of finite codimension

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  • T. S. S. R. K. Rao

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.

Suggested Citation

  • T. S. S. R. K. Rao, 2003. "Proximinal subspaces of A ( K ) of finite codimension," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:417904
    DOI: 10.1155/S0161171203212308
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