Isometries for the Legendre-Fenchel transform

Attouch, Hédy; Wets, Roger J.-B.

doi:10.1090/S0002-9947-1986-0837797-X

Isometries for the Legendre-Fenchel transform
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by Hédy Attouch and Roger J.-B. Wets PDF

Trans. Amer. Math. Soc. 296 (1986), 33-60 Request permission

Abstract:

It is shown that on the space of lower semicontinuous convex functions defined on ${R^n}$, the conjugation map—the Legendre-Fenchel transform—is an isometry with respect to some metrics consistent with the epi-topology. We also obtain isometries for the infinite dimensional case (Hilbert space and reflexive Banach space), but this time they correspond to topologies finer than the Moscoepi-topology.

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approximations inf-convolutives associées à un référentiel

Sur la fonction d’appui des ensembles convexes dans un espace localement convexe

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Extended real analysis