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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On elements with negative squares

Authors: Ralph DeMarr and Arthur Steger
Journal: Proc. Amer. Math. Soc. 31 (1972), 57-60
MathSciNet review: 0289390
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Abstract | References | Additional Information

Abstract: We prove that in a partially ordered linear algebra no element can have a square which is the negative of an order unit. In particular, the square of a real matrix cannot consist entirely of negative entries. We generalize the well-known theorem that the complex numbers admit no lattice order.

References [Enhancements On Off] (What's this?)

  • [1] Ralph DeMarr, On partially ordering operator algebras, Canad. J. Math. 19 (1967), 636–643. MR 0212579
  • [2] L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0171864
  • [3] Peter Lancaster, Theory of matrices, Academic Press, New York-London, 1969. MR 0245579

Additional Information

Keywords: Partially ordered linear algebras, matrix inequalities, linear operators
Article copyright: © Copyright 1972 American Mathematical Society