On the Young-Fenchel transform for convex functions
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- by Gerald Beer PDF
- Proc. Amer. Math. Soc. 104 (1988), 1115-1123 Request permission
Abstract:
Let $\Gamma (X)$ be the proper lower semicontinuous convex functions on a reflexive Banach space $X$. We exhibit a simple Vietoris-type topology on $\Gamma (X)$, compatible with Mosco convergence of sequences of functions, with respect to which the Young-Fenchel transform (conjugate operator) from $\Gamma (X)$ to $\Gamma ({X^*})$ is a homeomorphism. Our entirely geometric proof of the bicontinuity of the transform halves the length of Mosco’s proof of sequential bicontinuity, and produces a stronger result for nonseparable spaces.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 1115-1123
- MSC: Primary 49A50; Secondary 26E25, 46B99, 54B20
- DOI: https://doi.org/10.1090/S0002-9939-1988-0937844-8
- MathSciNet review: 937844