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arXiv · 2509.02787

The Berger-Wang formula for order-preserving homogeneous maps on cones

Brian Lins·Aljoša Peperko
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Abstract

We prove that the joint spectral radius and generalized spectral radius are equal for any bounded, equicontinuous family of order-preserving, homogeneous maps on a polyhedral cone. We also consider conditions which guarantee that the semigroup generated by a family of order-preserving, homogeneous maps is bounded when its generalized spectral radius $r(\mathcal{A}) = 1$. Finally, we extend the notions of joint and generalized spectral subradii to the setting of homogeneous maps on wedges.

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Brian Lins, Aljoša Peperko. 2025-09-02. The Berger-Wang formula for order-preserving homogeneous maps on cones. https://arxiv.org/abs/2509.02787

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