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Proximinality in Banach spaces |
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| Authors: | Pradipta Bandyopadhyay Darapaneni Narayana |
| Institution: | a Stat-Math Division, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India b Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, PR China c Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA d Department of Mathematics, Indian Institute of Science, Bangalore 560012, India |
| 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. |
| Keywords: | Approximatively τ-compact τ-Strongly Chebyshev Metric projection τ-Almost locally uniformly rotund |
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