Set-Valued Analysis

, Volume 15, Issue 3, pp 307–315 | Cite as

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

  • Francisco J. Aragón ArtachoEmail author


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.

Key words

convex process sublinear mapping norm duality inner norm outer norm 

Mathematics Subject Classifications (2000)

49J53 47H04 54C60 


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversity of AlicanteAlicanteSpain

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