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Strong proximinality and renormings


Author: Darapaneni Narayana
Journal: Proc. Amer. Math. Soc. 134 (2006), 1167-1172
MSC (2000): Primary 46B20
Published electronically: October 25, 2005
MathSciNet review: 2196053
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Abstract: We characterize finite-dimensional normed linear spaces as strongly proximinal subspaces in all their superspaces. A connection between upper Hausdorff semi-continuity of metric projection and finite dimensionality of subspace is given.


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Additional Information

Darapaneni Narayana
Affiliation: Stat-Math Unit, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India
Address at time of publication: Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Email: dnarayana76@hotmail.com, narayana@math.iisc.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08151-7
Keywords: Strongly proximinal subspace, reflexive space, finite-dimensional space.
Received by editor(s): August 2, 2004
Received by editor(s) in revised form: November 11, 2004
Published electronically: October 25, 2005
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.