Invertibly Positive Linear Operators on Spaces of Continuous Functions.

Thomas A. Brown, M. L. Juncosa, Victor Klee

ResearchPublished 1968

A proof that any positive linear transformation of a space of continuous functions with a positive inverse has a certain specific form. The characterization is the same as that found by Kaplansky and others, but here it is obtained under weaker assumptions as to the topological space X and the linear space F of real-valued functions. The study was motivated by a problem in logistics, which, mathematically, was to find conditions necessary and sufficient for a positive matrix to have one of its powers equal to the identity matrix. (The results are used in Theorem II of RM-5385, Aircrew Ratio Studies.) 26 pp. Ref. (MW)

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Brown, Thomas A., M. L. Juncosa, and Victor Klee, Invertibly Positive Linear Operators on Spaces of Continuous Functions. Santa Monica, CA: RAND Corporation, 1968. https://www.rand.org/pubs/research_memoranda/RM5374.html.
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