A Note on Dominant Contractions of Jordan Algebras

Details A Note on Dominant Contractions of Jordan Algebras A Note on Dominant Contractions of Jordan Algebras

2008-06-18

arxiv.org/abs/0806.2926v2

Turkish Journal of Mathematics, 34(2010), 85--93

Mathematics

Functional Analysis

9 pages. Turkish Journal of Mathematics (to appear)

Scientific paper

10.3906/mat-0810-24

In the paper we consider two positive contractions
$T,S:L^{1}(A,\tau)\longrightarrow L^{1}(A,\tau)$ such that $T\leq S$, here
$(A,\t)$ is a semi-finite $JBW$-algebra. If there is an $n_{0}\in\mathbb{N}$
such that $\|S^{n_{0}}-T^{n_{0}}\|<1$. Then we prove that $\|S^{n}-T^{n}\|<1$
holds for every $n\geq n_{0}.$

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