The limit of the spectral radius of block Toeplitz matrices with nonnegative entries

A bi-infinite sequence ...,t_–2,t_–1,t₀,t₁,t₂,... of nonnegativep×p matrices defines a sequence of block Toeplitz matricesT_n=(t_ik),n=1,2,...,, wheret_ik=t_k–i,i,k=1,...,n. Under certain irreducibility assumptions, we show that the limit of the spectral radius ofT_n, asn tends to infinity, is given by inf{()[0,]}, where () is the spectral radius of _jzt_j^j.Supported by SFB 343 Diskrete Strukturen in der Mathematik, Universität Bielefeld