[en] convex process ; sublinear mapping ; norm duality

[en] 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.

Luxembourg Centre for Systems Biomedicine (LCSB): Systems Biochemistry (Fleming Group)