Invertibly Positive Linear Operators on Spaces of Continuous Functions.

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

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback26 pages $20.00 $16.00 20% Web Discount

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)

This report is part of the RAND Corporation research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.