Abstract

We introduce an order relation on a locally convex cone P\mathcal{P} which implies the strict separation property for continuous linear functionals. Using this order we establish representations for P\mathcal{P} as a cone of extended real-valued functions and as a cone of convex subsets of a vector space.

Author information

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

Walter Roth

Dept. of Mathematics, University of Brunei Darussalam, Gadong BE1410, Brunei Darussalam

roth@fos.ubd.edu.bn

Keywords

  • Locally convex cones
  • separation properties
  • representation

Mathematics Subject Classification

46A20; 46A22

References

  1. K. Keimel, W. Roth: Ordered Cones and Approximation, Lecture Notes in Mathematics 1517, Springer-Verlag, Berlin et al. (1992).https://doi.org/10.1007/BFb0089190Google Scholar
  2. W. Roth: Hahn-Banach type theorems for locally convex cones, Journal of the Australian Math. Soc. (Series A) 68 (2000) 104–125.https://doi.org/10.1017/S1446788700001609Google Scholar

Suggested citation

W. Roth. “Separation Properties for Locally Convex Cones.” Journal of Convex Analysis 9 (2002), No. 1, 301–307. https://doi.org/10.68381/jca09018

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press LLC.