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Proceedings of the American Mathematical Society

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Isotone functions on partially ordered linear algebras with a multiplicative diagonal map

Authors: Taen Yu Dai and Ralph DeMarr
Journal: Proc. Amer. Math. Soc. 65 (1977), 11-15
MSC: Primary 06A70
MathSciNet review: 0485618
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Abstract: The diagonal of the product of two triangular matrices is the product of the diagonals of each matrix. This idea is used to characterize Dedekind $ \sigma $-complete lattice ordered linear algebras which admit isotone functions with familiar functional and order properties as possessed by the real-valued logarithm or root function.

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Keywords: Dedekind $ \sigma $-complete partially ordered linear algebra, lattice, diagonal, triangular matrices, matrix inequality, isotone functions
Article copyright: © Copyright 1977 American Mathematical Society

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