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1 results

  • Hahn-Banach Type Theorems for Locally Convex Cones

  • Part of
  • Walter Roth
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 68 / Issue 1 / February 2000
    Published online by Cambridge University Press:
    09 April 2009, pp. 104-125
    Print publication:
    February 2000
    • Article
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  • We prove Hahn-Banach type theorems for linear functionals with values in R∪{+∞} on ordered cones, Using the concept of locally convex cones, we provide a sandwich theorem involving sub- and superlinear functionals which are allowed to attain infinite values. It render general versions of well-known extension and separation results. We describe the range of all linear functionals sandwiched between given sub- and superlinear functionals on an ordered cone. The results are of interest even in vector spaces, since we consider sublinear functionals that may attain the value +∞.