# Accession Number:

## AD0678865

# Title:

## INVERTIBLY POSITIVE LINEAR OPERATORS ON SPACES OF CONTINUOUS FUNCTIONS,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1968-10-01

# Pagination or Media Count:

## 27.0

# Abstract:

A proof is given 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. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics