Semi-continuity of metric projections in $\ell _\infty$-direct sums
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Abstract:
Let $Y$ be a proximinal subspace of finite codimension of $c_0$. We show that $Y$ is proximinal in $\ell _\infty$ and the metric projection from $\ell _\infty$ onto $Y$ is Hausdorff metric continuous. In particular, this implies that the metric projection from $\ell _\infty$ onto $Y$ is both lower Hausdorff semi-continuous and upper Hausdorff semi-continuous.References
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Additional Information
- V. Indumathi
- Affiliation: Department of Mathematics, Pondicherry University, Kalapet, Pondicherry-605014, India
- Email: pdy_indumath@sancharnet.in
- Received by editor(s): October 23, 2003
- Received by editor(s) in revised form: December 18, 2003, and January 16, 2004
- Published electronically: November 1, 2004
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1441-1449
- MSC (2000): Primary 46B20, 41A50, 41A65
- DOI: https://doi.org/10.1090/S0002-9939-04-07690-7
- MathSciNet review: 2111943