LINEAR OPERATORS WITH POSITIVE INVERSE
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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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.