This handbook article presents a survey of the theory of positive operators. It is divided into the following sections: 1. Ordered vector spaces and Banach lattices. 2. Operators between Banach lattices. 3. When is every continuous operator regular? 4. Domination, compactness, and factorization. 5. Invariant subspaces of positive operators. 6. Compact-friendly operators and invariant subspaces. 7. Integral operators and invariant subspaces. 8. Applications.
For the entire collection see [Zbl 0970.46001].