A characterization of symmetric cones by an order-reversing property of the pseudoinverse maps

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Author(s)

Abstract

When a homogeneous convex cone is given, a natural partial order is introduced in the cone. We shall show that a homogeneous convex cone is a symmetric cone if and only if Vinberg's *-map and its inverse reverse the order. Actually our theorem is formulated in terms of the family of pseudoinverse maps including the *-map, and states that the above order-reversing property is typical of the *-map of a symmetric cone which coincides with the inverse map of the Jordan algebra associated with the symmetric cone.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 60(4), 1107-1134, 2008-10-01

    The Mathematical Society of Japan

References:  20

Codes

  • NII Article ID (NAID)
    10024905327
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    9691671
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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