Normed Julia set of bounded linear operators

Abstract

It is proved that the normed Julia set of a bounded linear operator T satisfying ∑_n=1^∞ ∕ |Tⁿ| < ∞ cannot be the whole space. It is also proved that there exists at least one bounded linear operator on ℓ^p, 1 ≤ p < ∞ such that the normed Julia set is the whole space.