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Convex composite representation of lower semicontinuous functions and renormings. (English. Abridged French version) Zbl 0801.46007
Summary: We show that each extended real-valued bounded below lower semicontinuous function on a Banach space \(X\) which admits an equivalent locally uniformly convex norm \(\| \;\|\) can be written as the composition of a lower semicontinuous convex function on \(X \times \mathbb{R}\) with the mapping \(S(x): = (x, - \| x \|^ 2)\) of \(X\) into \(X \times \mathbb{R}\). This result enables us in certain cases to reduce some problems to the convex case, which is often easier to handle.

46A55 Convex sets in topological linear spaces; Choquet theory
46B03 Isomorphic theory (including renorming) of Banach spaces