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Proceedings of the American Mathematical Society

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

 

 

Positive derivations on partially ordered linear algebra with an order unit


Authors: Taen Yu Dai and Ralph DeMarr
Journal: Proc. Amer. Math. Soc. 72 (1978), 21-26
MSC: Primary 06A70; Secondary 47B55
MathSciNet review: 0491402
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Abstract: We show that the range of a positive derivation on a Dedekind $ \sigma $-complete partially ordered linear algebra with an order unit is a set of generalized nilpotents. With additional assumptions on the algebra, we show that the algebra has an important property similar to a property of the algebra of upper triangular matrices.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0491402-4
Keywords: Dedekind $ \sigma $-complete partially ordered linear algebra, order unit, derivation, generalized nilpotent, matrix algebra, diagonal projection map
Article copyright: © Copyright 1978 American Mathematical Society