Sublinear growth of 1-cocycles and uniform convexity
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918403751542784 |
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| author | Thom, Andreas |
| author_facet | Thom, Andreas |
| contents | Let G be a finitely generated group, let $π\colon G \to {\rm GL}(E)$ be a uniformly bounded $c_0$-representation on a superreflexive Banach space $E$, and let $b \colon G \to E$ be a $1$-cocycle for $π$. Then $b$ has sublinear growth with respect to the word length. As a corollary we obtain the corresponding Hilbert space statement for strongly mixing unitary representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22049 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sublinear growth of 1-cocycles and uniform convexity Thom, Andreas Group Theory Functional Analysis 20F65, 22D12, 46B20 Let G be a finitely generated group, let $π\colon G \to {\rm GL}(E)$ be a uniformly bounded $c_0$-representation on a superreflexive Banach space $E$, and let $b \colon G \to E$ be a $1$-cocycle for $π$. Then $b$ has sublinear growth with respect to the word length. As a corollary we obtain the corresponding Hilbert space statement for strongly mixing unitary representations. |
| title | Sublinear growth of 1-cocycles and uniform convexity |
| topic | Group Theory Functional Analysis 20F65, 22D12, 46B20 |
| url | https://arxiv.org/abs/2603.22049 |