Por Nicholas Pischke (Technical University of Darmstadt).

I present proof-theoretic metatheorems that allow applications of proof mining to proofs involving the dual of a Banach space and its corresponding norm. This in particular relies on a new approach to treating suprema of certain bounded sets without any additional proof-theoretical strength. As a further extension, I use this system to provide a proof-theoretic metatheorem for gradients of Frechet-differentiable functions and their conjugates.

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