Uniform monotonicity of norms and the strong ``zero-two'' law
Extending previous results of Ornstein-Sucheston, Katznelson-Tzafriri and Wittmann the author proves the following theorem. Let E be a Banach lattice having uniformly monotone norm and let T be a positive contraction on E. If \(\| | T^{k+1}-T^ k| \| <0\) for some \(k\in {\mathbb{N}}\), then \(\lim_{n\to \infty}\| | T^{n+1}-T^ n| \| =0.\)
scientific article; zbMATH DE number 4127929