کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4607572 | 1337869 | 2011 | 24 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Best approximation in polyhedral Banach spaces Best approximation in polyhedral Banach spaces](/preview/png/4607572.png)
In the present paper, we study conditions under which the metric projection of a polyhedral Banach space XX onto a closed subspace is Hausdorff lower or upper semicontinuous. For example, we prove that if XX satisfies (∗)(∗) (a geometric property stronger than polyhedrality) and Y⊂XY⊂X is any proximinal subspace, then the metric projection PYPY is Hausdorff continuous and YY is strongly proximinal (i.e., if {yn}⊂Y{yn}⊂Y, x∈Xx∈X and ‖yn−x‖→dist(x,Y), then dist(yn,PY(x))→0).One of the main results of a different nature is the following: if XX satisfies (∗)(∗) and Y⊂XY⊂X is a closed subspace of finite codimension, then the following conditions are equivalent: (a) YY is strongly proximinal; (b) YY is proximinal; (c) each element of Y⊥Y⊥ attains its norm. Moreover, in this case the quotient X/YX/Y is polyhedral.The final part of the paper contains examples illustrating the importance of some hypotheses in our main results.
Journal: Journal of Approximation Theory - Volume 163, Issue 11, November 2011, Pages 1748–1771