Geodesic
The generalized joint spectral radius. A~geometric approach
Izvestiya. Mathematics , Tome 61 (1997) no. 5, pp. 995-1030.

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The properties of the joint spectral radius with an arbitrary exponent $p\in[1,+\infty]$ are investigated for a set of finite-dimensional linear operators $A_1,\dots,A_k$ \begin{align*} \widehat\rho_p=\lim_{n\to\infty}\biggl(\dfrac{1}{k^n}\,\sum_\sigma\|A_{\sigma (1)}\cdots A_{\sigma(n)}\|^p\biggr)^{\frac{1}{pn}},\quad p\infty, \\ \widehat\rho_{\infty}=\lim_{n\to\infty}\max_{\sigma}\|A_{\sigma(1)}\cdots A_{\sigma(n)}\|^{\frac{1}{n}}, \end{align*} where the summation and maximum extend over all maps $$ \sigma \colon\{1,\dots,n\}\to\{1,\dots,k\}. $$ Using the operation of generalized addition of convex sets, we extend the Dranishnikov–Konyagin theorem on invariant convex bodies, which has hitherto been established only for the case $p=\infty$. The paper concludes with some assertions on the properties of invariant bodies and their relationship to the spectral radius $\widehat \rho_p$. The problem of calculating $\widehat \rho_p$ for even integers $p$ is reduced to determining the usual spectral radius for an appropriate finite-dimensional operator. For other values of $p$, a geometric analogue of the method with a pre-assigned accuracy is constructed and its complexity is estimated. 
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     author = {V. Yu. Protasov},
     title = {The generalized joint spectral radius. {A~geometric} approach},
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     volume = {61},
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     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_5_a4/}
}
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V. Yu. Protasov. The generalized joint spectral radius. A~geometric approach. Izvestiya. Mathematics , Tome 61 (1997) no. 5, pp. 995-1030. http://geodesic.mathdoc.fr/item/IM2_1997_61_5_a4/

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