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Metric Projections and Polyhedral Spaces

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Abstract

We prove that if X is a Banach space and Y is a proximinal subspace of finite codimension in X such that the finite dimensional annihilator of Y is polyhedral, then the metric projection from X onto Y is lower Hausdorff semi continuous. In particular this implies that if X and Y are as above, with the unit sphere of the annihilator space of Y contained in the set of quasi-polyhedral points of X *, then the metric projection onto Y is Hausdorff metric continuous.

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Authors and Affiliations

  1. Department of Mathematics, Pondicherry University, Kalapet, Pondicherry, 605014, India

    V. Indumathi

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  1. V. Indumathi
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Correspondence to V. Indumathi.

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Partially supported under project DST/INT/US-NSF/RPO/141/2003.

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Indumathi, V. Metric Projections and Polyhedral Spaces . Set-Valued Anal 15, 239–250 (2007). https://doi.org/10.1007/s11228-006-0036-2

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  • DOI: https://doi.org/10.1007/s11228-006-0036-2

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