On the Uniform Zero-Two Law for Positive Contractions of Jordan Algebras - Mukhamedov, Farrukh (Eurasian Mathematical Journal, 2017)
Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform "zero-two" law: let \( T : L^1(X, F, μ) → L^1(X, F, μ) \) be a positive contraction. If for some \( m N {0} \) one has \( \|T^m+1 - T^m\| < 2 \), then \[ _n → ∞ \|T^n+1 - T^n\| = 0. \] In this paper we prove a non-associative version of the uniform "zero-two" law for positive contractions of \( L_1 \)-spaces associated with \( JBW \)-algebras.