On dominant contractions and a generalization of the zero–two law - Mukhamedov, Farrukh (Birkhäuser Basel, 2011)
Zaharopol proved the following result: let T, S : L1(X,F,μ) → L1(X,F,μ) be two positive contractions such that T ≤ S. If ||S−T|| < 1 then ||Sn − T n||<1 for all n ∈ N. In the present paper we generalize this result to multi-parameter contractions acting on L1. As an application of that result we prove a generalization of the “zero–two” law.