The limit of the spectral radius of block Toeplitz matrices with nonnegative entries |
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| Authors: | L Elsner S Friedland |
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| Institution: | (1) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany;(2) Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 60607-7045 Chicago, Illinois |
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| Abstract: | A bi-infinite sequence ...,t
–2,t
–1,t
0,t
1,t
2,... 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 
jz
t
j
j
.Supported by SFB 343  Diskrete Strukturen in der Mathematik , Universität Bielefeld |
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| Keywords: | Primary 15A42 15A48 47B35 47B65 |
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