Proximinal subspaces of A(K) of finite codimension
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. Whe...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203212308 |
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| author | T. S. S. R. K. Rao |
| author_facet | T. S. S. R. K. Rao |
| author_sort | T. S. S. R. K. Rao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-30b693aa7ada4707af8aaa6d8eb467a3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-30b693aa7ada4707af8aaa6d8eb467a32025-02-03T01:12:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003392501250510.1155/S0161171203212308Proximinal subspaces of A(K) of finite codimensionT. S. S. R. K. Rao0Statistics and Mathematics Unit, Indian Statistical Institute, RV College Post Office, Bangalore 560 059, IndiaWe 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.http://dx.doi.org/10.1155/S0161171203212308 |
| spellingShingle | T. S. S. R. K. Rao Proximinal subspaces of A(K) of finite codimension International Journal of Mathematics and Mathematical Sciences |
| title | Proximinal subspaces of A(K) of finite codimension |
| title_full | Proximinal subspaces of A(K) of finite codimension |
| title_fullStr | Proximinal subspaces of A(K) of finite codimension |
| title_full_unstemmed | Proximinal subspaces of A(K) of finite codimension |
| title_short | Proximinal subspaces of A(K) of finite codimension |
| title_sort | proximinal subspaces of a k of finite codimension |
| url | http://dx.doi.org/10.1155/S0161171203212308 |
| work_keys_str_mv | AT tssrkrao proximinalsubspacesofakoffinitecodimension |