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Semi-continuity of metric projections in $\ell_\infty$-direct sums


Author: V. Indumathi
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
Published electronically: November 1, 2004
MathSciNet review: 2111943
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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.


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Additional Information

V. Indumathi
Affiliation: Department of Mathematics, Pondicherry University, Kalapet, Pondicherry-605014, India
Email: pdy_indumath@sancharnet.in

DOI: https://doi.org/10.1090/S0002-9939-04-07690-7
Keywords: Proximinal, metric projection, lower semi-continuity, upper Hausdorff semi-continuity
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
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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