Rao, T. S. S. R. K. Proximinal subspaces of \(A(K)\) of finite codimension. (English) Zbl 1036.41014 Int. J. Math. Math. Sci. 2003, No. 39, 2501-2505 (2003). Summary: 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. Cited in 3 Documents MSC: 41A50 Best approximation, Chebyshev systems 46B20 Geometry and structure of normed linear spaces PDFBibTeX XMLCite \textit{T. S. S. R. K. Rao}, Int. J. Math. Math. Sci. 2003, No. 39, 2501--2505 (2003; Zbl 1036.41014) Full Text: DOI EuDML