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Proceedings of the American Mathematical Society

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

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1977-0485618-X
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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DOI: https://doi.org/10.1090/S0002-9939-1977-0485618-X
Keywords: Dedekind $ \sigma $-complete partially ordered linear algebra, lattice, diagonal, triangular matrices, matrix inequality, isotone functions
Article copyright: © Copyright 1977 American Mathematical Society