On positive unipotent operators on Banach lattices

Abstract

Let T T be a positive operator on a complex Banach lattice. We prove that T T is greater than or equal to the identity operator I I if \[ lim n → ∞ n ‖ ( T − I ) n ‖ 1 / n = 0. \lim _{n \rightarrow \infty } n \, \|(T - I)^n\|^{1/n} = 0. \]