Asymptotic behavior of positive operators on Banach lattices (Q1588017)

This is a nice short survey dealing with some asymptotic properties of positive operators on Banach lattices. The new results are provided with sketches of proofs. A sample result: Theorem 12. Let \(0\leq S\leq T\) be two operators on a Banach lattice \(E\) with order continuous norm. If \(T\) is strongly stable (resp. almost periodic), then \(S\) has the same property. Recall that an operator \(T\) is strongly stable (resp. almost periodic) if for each \(x\in E\) the sequence \(\{T^nx\}\) converges in norm (resp. is norm-precompact). The paper contains a number of open problems.