On products of unbounded collections of matrices Original Research Article

Families image and image of n × n complex matrices with bounded products are studied. In particular, it is shown that if A = Bk := {B1B2 … Bk : Bi set membership, variant image (i = 1, 2, …, k)} is bounded for some k, then Bm is bounded for all m greater-or-equal, slanted n. The latter result is used to extend the relation image due to I. Daubechies and J. C. Lagarias for unbounded families image, where image := sup{tB1 … Bkshort parallel : Bi set membership, variant image (i = 1, …, k)} and K = 1, 2,…}.