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 On a multi-parametric generalization of the uniform zero-two law in $L^1$-spaces Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 1819-1826 https://doi.org/10.4134/BKMS.2015.52.6.1819Published online November 30, 2015 Farrukh Mukhamedov P.O. Box, 141, 25710, Kuantan Abstract : Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform zero-two" law: let $T:L^1(X,{\cf},\m)\to L^1(X,{\cf},\m)$ be a positive contraction. If for some $m\in\bn\cup\{0\}$ one has $\|T^{m+1}-T^m\|<2$, then $$\lim\limits_{n\to\infty}\|T^{n+1}-T^n\|=0.$$ 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 $L^1$-contractions. Keywords : multi parametric, positive contraction, zero-two" law MSC numbers : 47A35, 17C65, 46L70, 46L52, 28D05 Full-Text :