Abstract
Families A and B of n × n complex matrices with bounded products are studied. In particular, it is shown that if A = B k := { B 1 B 2 … B k : B i ∈ B (i = 1, 2, …, k)} is bounded for some k, then B m is bounded for all m ⩾ n. The latter result is used to extend the relation lim sup k → x ϱk(B) 1 k ⩽ ϱk(B) 1 k due to I. Daubechies and J. C. Lagarias for unbounded families B , where \\ ̂ g9 k(B) := sup{t|B 1 … B k∥ : B i ∈ B (i = 1, …, k)} and k = 1, 2,…}.
Full Text
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call