On power bounded operators
The main result asserts that, for any contraction T on an arbitrary Banach space X, \(\| T^ n-T^{n+1}\| \to \infty\), if and only if the spectrum of T has no points on the unit circle except perhaps \(z=1\). This theorem is extended for \(\phi (T)T^ n\), where \(\phi\) is a function of spectral synthesis on the unit circle. As an application, we generalize the so-called ''zero-two'' law of Ornstein and Sucheston and Zaharopol to positive contraction on a very large class of Banach lattices.
zero-two law of Ornstein and Sucheston and Zaharopol
function of spectral synthesis on the unit circle
scientific article; zbMATH DE number 3988025