Let T be a positive power-bounded operator on a Banach lattice. We prove: (i) If infn ∥Tn(I - T)∥ < 2, then there is a k ≥ 1 such that limn→∞ ∥Tn(I - Tk)∥ = 0. (ii) limn→∞ ∥Tn(I - T)∥ = 0 if (and only if) infn ∥Tn(I - T)∥ < √3.
ASJC Scopus subject areas
- Mathematics (all)