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A New and Self-Contained Proof of Borwein’s Norm Duality Theorem

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Abstract

Borwein’s norm duality theorem establishes the equality between the outer (inner) norm of a sublinear mapping and the inner (outer) norm of its adjoint mappings. In this note we provide an extended version of this theorem with a new and self-contained proof relying only on the Hahn-Banach theorem. We also give examples showing that the assumptions of the theorem cannot be relaxed.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, University of Alicante, 03071, Alicante, Spain

    Francisco J. Aragón Artacho

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  1. Francisco J. Aragón Artacho
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Correspondence to Francisco J. Aragón Artacho.

Additional information

This author is supported by Grant BES-2003-0188 from FPI Program of MEC (Spain).

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Aragón Artacho, F.J. A New and Self-Contained Proof of Borwein’s Norm Duality Theorem. Set-Valued Anal 15, 307–315 (2007). https://doi.org/10.1007/s11228-006-0040-6

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  • DOI: https://doi.org/10.1007/s11228-006-0040-6

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