Geodesic
On the uniform zero-two law for positive contractions of Jordan algebras
Eurasian mathematical journal, Tome 8 (2017) no. 4, pp. 55-62

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Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform "zero-two" law: let $T:\ L^1(X,\mathcal{F}, \mu)\to L^1(X,\mathcal{F}, \mu)$ be a positive contraction. If for some $m\in\mathbb{N}\cup\{0\}$ one has $||T^{m+1}-T^m||2$, then $$ \lim_{n\to\infty}|| T^{m+1}-T^m||=0. $$ In this paper we prove a non-associative version of the unform "zero-two" law for positive contractions of $L_1$-spaces associated with $JBW$-algebras. 
@article{EMJ_2017_8_4_a6,
     author = {F. Mukhamedov},
     title = {On the uniform zero-two law for positive contractions of {Jordan} algebras},
     journal = {Eurasian mathematical journal},
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     url = {http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a6/}
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F. Mukhamedov. On the uniform zero-two law for positive contractions of Jordan algebras. Eurasian mathematical journal, Tome 8 (2017) no. 4, pp. 55-62. http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a6/