A Note on Dominant Contractions of Jordan Algebras

Abstract

In the paper we consider two positive contractions $T,S:L^1(A,\tau )⟶L^1(A,\tau )$ such that $T\le S$, here $(A,\t)$ is a semi-finite $JBW$-algebra. If there is an $n_0\in \mathbb{N}$ such that $\Vert S^{n_0}-T^{n_0}\Vert <1$. Then we prove that $\Vert S^n-T^n\Vert <1$ holds for every $n\ge n_0.$

9 pages. Turkish Journal of Mathematics (to appear)

Cited by in corpus (2)

• On dominant contractions and a generalization of the zero-two law
• On Limit theorems in $JW$- algebras