Abstract

We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duality theorem. Most of the results are about affine functions defined on convex subsets of vector spaces, rather than linear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duality theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper also contains some new results about metrizable topological vector spaces that are not necessarily locally convex.

Author information

Contact details are reproduced from the original publication and may be historical.

Stephen Simons

Dept. of Mathematics, University of California, Santa Barbara, CA 93106-3080, U.S.A.

simons@math.ucsb.edu

Keywords

  • Asymmetric sandwich theorem
  • Hahn-Banach theorem
  • Fenchel duality theorem
  • affine functions
  • metrizable topological vector spaces
  • local convexity

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Suggested citation

S. Simons. “The Asymmetric Sandwich Theorem.” Journal of Convex Analysis 20 (2013), No. 1, 107–124. https://doi.org/10.68381/jca20007

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.