LINEAR OPERATORS WITH POSITIVE INVERSE
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. 3:365-376, 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1961
- Accession Number
- AD0260203
Entities
People
- J. Schroder
Organizations
- University of Wisconsin–Madison