Invertibly Positive Linear Operators on Spaces of Continuous Functions.

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

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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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