# Accession Number:

## AD0260203

# Title:

## LINEAR OPERATORS WITH POSITIVE INVERSE

# Descriptive Note:

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1961-05-01

# Pagination or Media Count:

## 1.0

# Abstract:

The theorem considers an operator M on a partially ordered space into such a space. The question at issue is determination of those conditions under which the equation, Mu is less than or equal to Mv, implies the equation, u is less than or equal to v. An operator with this property is called the monotonic type L. Collatz. Aufgaben monotoner Art. Arch. Math. 3365-376, 1952. For linear operators the conditions for a monotonic operator have two equivalent forms 1 the equation, Mu is greater than or equal to zero, implies the equation, u is greater than or equal to zero and 2 M has a positive inverse. It is shown that nonlinear operators can be proved to be of monotonic type if certain linear operators have this property.