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Upper Semicontinuity of Duality and Preduality Mappings

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Computational and Analytical Mathematics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 50))

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Abstract

In their paper studying Hausdorff weak upper semicontinuity of duality and preduality mappings on the dual of a Banach space, Godefroy and Indumathi related these by an interesting geometrical property. This property actually characterises Hausdorff upper semicontinuity of the preduality mapping. When the duality mapping is Hausdorff upper semicontinuous with weakly compact image, we investigate how this same property persists with natural embedding into higher duals.

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Acknowledgements

I would like to thank Scott Sciffer and Rebecca Smith for their assistance in the preparation of this paper.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, The University of Newcastle, New South Wales, 2308, Australia, Newcastle

    J. R. Giles

Authors
  1. J. R. Giles
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Corresponding author

Correspondence to J. R. Giles .

Editor information

Editors and Affiliations

  1. Lawrence Berkeley National Laboratory, Berkeley, USA

    David H. Bailey

  2. Mathematics, University of British Columbia, Kelowna, British Columbia, Canada

    Heinz H. Bauschke

  3. Dept. Mathematics & Statistics, Simon Fraser University, Burnaby, British Columbia, Canada

    Peter Borwein

  4. Mathematics, University of Florida, Gainesville, Florida, USA

    Frank Garvan

  5. Mathematics and Computer Science, University of Limoges, Limoges, France

    Michel Théra

  6. Mathematics and Computer Science Department, La Sierra University, Riverside, California, USA

    Jon D. Vanderwerff

  7. Dept. Combinatorics & Optimization, University of Waterloo Faculty of Mathematics, Waterloo, Ontario, Canada

    Henry Wolkowicz

Additional information

To celebrate Jonathan Borwein’s 60th birthday

Communicated By Jon D. Vanderwerff.

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Giles, J.R. (2013). Upper Semicontinuity of Duality and Preduality Mappings. In: Bailey, D., et al. Computational and Analytical Mathematics. Springer Proceedings in Mathematics & Statistics, vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7621-4_18

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