International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 39, Pages 2501-2505

Proximinal subspaces of A(K) of finite codimension

T. S. S. R. K. Rao

Statistics and Mathematics Unit, Indian Statistical Institute, RV College Post Office, Bangalore 560 059, India

Received 30 December 2002

Copyright © 2003 T. S. S. R. K. Rao. 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.


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.