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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0289390-3
MathSciNet review: 0289390
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0289390-3
Keywords: Partially ordered linear algebras, matrix inequalities, linear operators
Article copyright: © Copyright 1972 American Mathematical Society

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