On the spectral radius of the product of matrix exponentials (Q923681)

The author proves that \textit{J. E. Cohen}, \textit{S. Friedland}, \textit{T. Kato} and \textit{F. P. Kelly}'s conjecture [ibid. 45, 55-95 (1982; Zbl 0489.15007)] about convexity of the logarithm of the spectral radius \(F(t)=\log r(e^{At}\cdot e^{Bt})\) for real \(t>0\) when A is an \(n\times n\) nonnegative matrix and B is an \(n\times n\) real diagonal matrix is false for all \(n\geq 3\).