The Berger-Wang formula for order-preserving homogeneous maps on cones
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911135982157824 |
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| author | Lins, Brian Peperko, Aljoša |
| author_facet | Lins, Brian Peperko, Aljoša |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02787 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Berger-Wang formula for order-preserving homogeneous maps on cones Lins, Brian Peperko, Aljoša Functional Analysis 47H07, 47J10 (Primary), 15A80, 15B48 (Secondary) 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. |
| title | The Berger-Wang formula for order-preserving homogeneous maps on cones |
| topic | Functional Analysis 47H07, 47J10 (Primary), 15A80, 15B48 (Secondary) |
| url | https://arxiv.org/abs/2509.02787 |