The limit of the spectral radius of block Toeplitz matrices with nonnegative entries
Elsner, Ludwig
Elsner
Ludwig
Friedland, Shmuel
Friedland
Shmuel
A bi-infinite sequence ..., t(-2), t(-1), t(0), t(1), t(2), ... of nonnegative p x p matrices defines a sequence of block Toeplitz matrices T-n = (t(ik)), n = 1, 2, ...,, where t(ik) = t(k-i), i, k = 1, ..., n. Under certain irreducibility assumptions, we show that the limit of the spectral radius of T-n, as n tends to infinity, is given by inf {sigma(xi) : xi epsilon [0, infinity]}, where sigma(xi) is the spectral radius of Sigma(j epsilon Z)t(j)xi(j).
36
2
193-200
193-200
BirkhĂ¤user
2000