Abstract
Fiedler and Ptak called a cone minimal if it is n-dimensional and has n + 1 extreme rays. We call a cone almost-minimal if it is n-dimensional and has n + 2 extreme rays. Duality properties stemming from the use of Gale pairs lead to a general technique for identifying the extreme cone-preserving (positive) operators between polyhedral cones. This technique is most effective for cones with dimension not much smaller than the number of their extreme rays. In particular, the Fiedler–Ptak characterization of extreme positive operators between minimal cones is extended to the following cases: (i) operators from a minimal cone to an arbitrary polyhedral cone, and (ii) operators from an almost-minimal cone to a minimal cone.
Published Version
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