Invariant subspaces of linear transformations
Invariant subspaces of linear transformations
A (not necessarily bounded) linear transformation on a Banach space is intransitive if it has a proper closed invariant subspace; otherwise it is transitive.The general invariant subspace problem asks whether a separable infinite- dimensional Banach space can possess bounded transitive linear transforma- tions.Shields [-5, Theorem 1] constructed a transitive (not …