Dobrushin Coefficients of Ergodicity and Asymptotically Stable L 1-Contractions

We extend an inequality (which involves the Dobrushin coefficient of ergodicity; see Cohen et al.⁽⁴⁾) to any linear bounded operator with domain and codomain L ¹-spaces. We use the extended Dobrushin coefficient of ergodicity, that appears in the inequality, in order to obtain sufficient conditions for the uniform asymptotic stability of a positive contraction of an L ¹-space. We conclude the paper by studying a class of strongly asymptotically stable positive contractions.