@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}
}

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.