EN
Let V be the classical Volterra operator on L²(0,1), and let z be a complex number. We prove that I-zV is power bounded if and only if Re z ≥ 0 and Im z = 0, while I-zV² is power bounded if and only if z = 0. The first result yields
$||(I-V)ⁿ - (I-V)^{n+1}|| = O(n^{-1/2})$ as n → ∞,
an improvement of [Py]. We also study some other related operator pencils.