Ideal-triangularizability of semigroups of positive operators (Q1037201)

A positive operator \(T\) acting on a Banach lattice \(E\) is called ideal-triangularizable if it admits a maximal chain of invariant closed ideals of \(E\). The paper under review discusses the question under which conditions a multiplicative semigroup \(\mathcal{S}\) of ideal-triangularizable operators is simultaneously ideal-triangularizable. For example, it is proved that this is the case when \(E\) has order continuous norm. Also, a semigroup \(\mathcal{S}\) of positive compact operators on a Banach lattice with order continuous norm is ideal-triangularizable if and only if every pair \(\{S,T\}\) of operators in \(\mathcal{S}\) is ideal-triangularizable.