On Stability of Polynomially Bounded Operators - Muraz, G.; Vu, Quoc Phong (Журнал математичної фізики, аналізу, геометрії, 2007)
We prove that if T is a polynomially bounded operator and the peripheral spectrum of T has zero measure, then Tnx → 0 for all x in X if and only if T* has no nontrivial invariant subspace on which it is invertible and doubly power bounded.Mathematics Subject Classification: 47A15.