On elements with negative squares
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- by Ralph DeMarr and Arthur Steger PDF
- Proc. Amer. Math. Soc. 31 (1972), 57-60 Request permission
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
- Ralph DeMarr, On partially ordering operator algebras, Canadian J. Math. 19 (1967), 636–643. MR 212579, DOI 10.4153/CJM-1967-057-6
- 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
- Peter Lancaster, Theory of matrices, Academic Press, New York-London, 1969. MR 0245579
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 57-60
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289390-3
- MathSciNet review: 0289390