The Discrete Hille–Yosida Space and the Asymptotic Behaviour of Individual Orbits of Linear Operators

A discrete analog of a construction of the Hille–Yosida space is used to obtain results on the asymptotic behaviour of individual orbits of generally unbounded operators. Results on power-bounded linear operators on a Banach space are applied to the restriction of the operator on the Hille–Yosida space. The same method is used to obtain an individual variant of the Katznelson–Tzafriri Theorem. Continuous analogs for some of these results will be presented elsewhere.