The zero-two law for positive contractions is valid in all Banach lattices
The author uses techniques from the theory of Banach lattices and positive operators in order to extend the so-called zero-two law [see e.g. \textit{Y. Katznelson} and \textit{L. Tzafriri}, J. Funct. Anal. 68, 313- 328 (1986; Zbl 0611.47005)] to arbitrary Banach lattices. More precisely, let T be a positive contraction on some complex Banach lattice X. Then either \(\lim_{n\to \infty}\| T^ n-T^{n+1}\| =0\) or \(\| T^ n-T^{n+1}\|_ r=2\) for all \(n\in {\mathbb{N}}\) whre \(\| \cdot \|_ r\) denotes the ``regular'' norm \(\| R\|_ r:=\inf \{\| S_ 1+S_ 2\|:R=S_ 1-S_ 2\), \(0\leq S_ i\in {\mathcal L}(X)\}\).
scientific article; zbMATH DE number 4073801