A note on dominant contractions of Jordan algebras - Mukhamedov, Farrukh; Temir, Seyit; Akin, Hasan (The Scientific and Technological Research Council of Turkey, 2010)
We consider two positive contractions T, S : L1(A, τ) −→ L1(A, τ) such that T ≤ S, here (A, τ) is a semi-finite JBW-algebra. If there is an n0 ∈ N such that ||S^{n_0} − T^{n_0}|| < 1, we prove that ||S^n − T^n|| < 1 holds for every n ≥ n_0.