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

MathSciNet review:
565331

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that a Dedekind -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.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0565331-0

Keywords:
Dedekind -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