Modulus hyperinvariant ideals for a finitely quasinilpotent operators

Abstract

Let $X$ be a Banach space with an unconditional basis, and let ${\mathcal C}\neq \{0\}$ be a collection of continuous linear operators with modulus on $X$ that is finitely modulus-quasinilpotent at a non-zero positive vector. Then ${\mathcal C}$ and its right modulus sub-commutant ${\mathcal C}^{'}_{\mbox{m}}$ have a common non-trivial invariant closed ideal.