The Positive Fixed Points of Banach Lattices
The Positive Fixed Points of Banach Lattices
Let $Z$ be a Banach lattice endowed with positive cone $C$ and an order-continuous norm $|| \cdot ||$. Let $G$ be a left-amenable semigroup of positive linear endomorphisms of $Z$. Then the positive fixed points ${C_0}$ of $Z$ under $G$ form a lattice cone, and their linear span ${Z_0}$ is …