Proximinality in Banach spaces

Bandyopadhyay, Pradipta and Li, Yongjin and Lin, Bor-Luh and Narayana, Darapaneni (2008) Proximinality in Banach spaces. In: Journal of Mathematical Analysis and Applications, 341 (1). pp. 309-317.

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Abstract

In this paper, we study approximatively τ-compact and τ-strongly Chebyshev sets, where τ is the norm or the weak topology. We show that the metric projection onto τ-strongly Chebyshev sets are norm-τ continuous. We characterize approximatively τ-compact and τ-strongly Chebyshev hyperplanes and use them to characterize factor reflexive proximinal subspaces in τ-almost locally uniformly rotund spaces. We also prove some stability results on approximatively τ-compact and τ-strongly Chebyshev subspaces.

Item Type:	Journal Article
Publication:	Journal of Mathematical Analysis and Applications
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Approximatively τ-compact;τ-Strongly Chebyshev;Metric projection;τ-Almost locally uniformly rotund.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Mar 2010 07:33
Last Modified:	19 Sep 2010 05:58
URI:	http://eprints.iisc.ac.in/id/eprint/26685

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