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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 35 #3450. MR 0212579 (35:3450)
  • [2] L. Fuchs, Partially ordered algebraic systems, Pergamon Press, New York, 1963, p. 143. MR 30 #2090. MR 0171864 (30:2090)
  • [3] P. Lancaster, Theory of matrices, Academic Press, New York, 1969, pp. 282-291. MR 39 #6885 MR 0245579 (39:6885)

Additional Information

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

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