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Elementary functional equations on partially ordered linear algebra


Author: Taen Yu Dai
Journal: Proc. Amer. Math. Soc. 79 (1980), 167-173
MSC: Primary 06F25; Secondary 39B20, 39B50
DOI: https://doi.org/10.1090/S0002-9939-1980-0565331-0
MathSciNet review: 565331
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Abstract: Suppose that a Dedekind $ \sigma $-complete partially ordered linear algebra A admits a function with familiar functional and order properties as possessed by the real-valued exponential, logarithm, root or power function on the real line. Then A can be characterized as an algebra of almost finite extended-real-valued continuous functions defined on some proper topological space.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0565331-0
Keywords: Dedekind $ \sigma $-complete partially ordered linear algebra, Cauchy functional equations, isotone functions, algebra of almost finite extended-real-valued continuous functions, matrix inequality
Article copyright: © Copyright 1980 American Mathematical Society

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