Inner spectral radius of positive operator matrices

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Spectral radius, symmetric and positive matrices

If ρ(A) > 1, then lim n→∞ ‖A‖ =∞. Proof. Recall that A = CJC−1 for a matrix J in Jordan normal form and regular C, and that A = CJnC−1. If ρ(A) = ρ(J) < 1, then J converges to the 0 matrix, and thus A converges to the zero matrix as well. If ρ(A) > 1, then J has a diagonal entry (J)ii = λ n for an eigenvalue λ such that |λ| > 1, and if v is the i-th column of C and v′ the i-th row of C−1, then ...

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ژورنال

عنوان ژورنال: Banach Journal of Mathematical Analysis

سال: 2008

ISSN: 1735-8787

DOI: 10.15352/bjma/1240336278