From local to global triangularization
A collection of bounded linear operators is said to be triangularizable if there exists a maximal subspace chain consisting of subspaces which are invariant under all operators in the collection. The main result of this paper asserts that a semigroup of operators in a Schatten \(p\)-class is triangularizable if every pair of operators in the semigroup is triangularizable. In other words, one can automatically pass from the local to global triangularization. The authors also establish a ``block triangularization'' theorem for algebras of compact operators, whose consequences include several necessary and sufficient conditions for triangularization of such algebras.
scientific article; zbMATH DE number 1046933
scientific article