International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 417904 | https://doi.org/10.1155/S0161171203212308

T. S. S. R. K. Rao, "Proximinal subspaces of of finite codimension", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 417904, 5 pages, 2003. https://doi.org/10.1155/S0161171203212308

Proximinal subspaces of A(K) of finite codimension

Received30 Dec 2002

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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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