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

• Kai Chifune

  Faculty of Mathematics, Kyushu University

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

  The Mathematical Society of Japan

Keywords

• homogeneous convex cone
• symmetric cone
• partial order
• pseudoinverse map
• duality mapping

Details

• CRID: 1390282680091426048
• NII Article ID: 10024905327
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/06041107
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 9691671
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I9691671
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed