Random Products of Contractions in Banach Spaces

  title={Random Products of Contractions in Banach Spaces},
  author={Joseph Dye and M. A. Khamsi and Simeon Reich},
We show that the random product of a finite number of ( W) contractions converges weakly in all smooth reflexive Banach spaces. If one of the contractions is compact, then the convergence is uniform. Let (A, | • |) be a (real) Banach space and T: X —> X a linear operator. Recall that T is called a contraction if \Tv\ < \v\ for all vectors v in A. We say that a contraction T satisfies condition (W) if whenever {vn} is bounded and \vn\ \Tvn\ —<■ 0, it follows that the weak lim„_00(v„ Tvn) = 0… CONTINUE READING


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