The uniform zero-two law for positive operators in Banach lattices
Volume 131 / 1998
Studia Mathematica 131 (1998), 149-153
DOI: 10.4064/sm-131-2-149-153
Abstract
Let T be a positive power-bounded operator on a Banach lattice. We prove: (i) If $inf_n ||T^n(I-T)|| < 2$, then there is a k ≥ 1 such that $lim_{n→∞} ||T^n(I-T^k)|| = 0. (ii) $lim_{n→∞} ||T^n(I-T)|| = 0$ if (and only if) $inf_n ||T^n(I-T)|| < √3$.
