International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 39, Pages 2501-2505
Proximinal subspaces of of finite codimension
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 of finite codimension in the context of the space of affine continuous functions on a compact convex set . We give an example to show that a simple-minded analogue of Garkavi's result fails for these spaces. When is a metrizable Choquet simplex, we give a necessary and sufficient condition for a boundary measure to attain its norm on . We also exhibit proximinal subspaces of finite codimension of when the measures are supported on a compact subset of the extreme boundary.