## Abstract

Fiedler and Pták 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–Pták 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.

Original language | English |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | North-Holland Mathematics Studies |

Volume | 87 |

Issue number | C |

DOIs | |

State | Published - 1 Jan 1984 |

Externally published | Yes |

### Bibliographical note

Funding Information:* Due to space limitations this paper gives the main definitions and resuIts of the work. For proofs and further details the reader is referred to [l]. Research supported in part by the Technion’s Vice President for Research Grant no. 100-473.

### Funding

* Due to space limitations this paper gives the main definitions and resuIts of the work. For proofs and further details the reader is referred to [l]. Research supported in part by the Technion’s Vice President for Research Grant no. 100-473.

Funders | Funder number |
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Technion-Israel Institute of Technology | 100-473 |