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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 296 (1986), 33-60
  • MSC: Primary 49A50; Secondary 52A40, 58E30, 90C25
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0837797-X
  • MathSciNet review: 837797