A New and Self-Contained Proof of Borwein’s Norm Duality Theorem
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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 wordsconvex process sublinear mapping norm duality inner norm outer norm
Mathematics Subject Classifications (2000)49J53 47H04 54C60
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