Bounded semigroups of matrices

@article{Berger1992BoundedSO,
  title={Bounded semigroups of matrices},
  author={M. Berger and Y. Wang},
  journal={Linear Algebra and its Applications},
  year={1992},
  volume={166},
  pages={21-27}
}
  • M. Berger, Y. Wang
  • Published 1992
  • Mathematics
  • Linear Algebra and its Applications
  • In this note are proved two conjectures of Daubechies and Lagarias. The first asserts that if Z is a bounded set of matrices such that all left infinite products converge, then 8 generates a bounded semigroup. The second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices. One definition involves the conventional spectral radius, and one involves the operator norm. 
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      each d(j) is generated by Z%(j) = {M(j) : M E I;), after similarity reduction; and thus our result follows now from Lemma II(c)
      • each d(j) is generated by Z%(j) = {M(j) : M E I;), after similarity reduction; and thus our result follows now from Lemma II(c)