On a multi-parametric generalization of the uniform zero-two law in L1-spaces - Mukhamedov, Farrukh (Korean Mathematical Society, 2015)
Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform “zero-two” law: let T : L1 (X, F, µ) → L1 (X, F, µ) be a positive contraction. If for some m ∈ N∪{0} one has kT m+1−T mk < 2, then lim n→∞ kT n+1 − T nk = 0. There are many papers devoted to generalizations of this law. In the present paper we provide a multi-parametric generalization of the uniform zero-two law for L1 -contractions