Bounded Semigroups of Matrices

  title={Bounded Semigroups of Matrices},
  author={Marc and A. Berger},
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. The occurrence of convergent infinite products of matrices pervades many current… CONTINUE READING
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