Uniformly affine actions on Banach spaces: growth of cocycles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908756869120000 |
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| author | Boucher, Kevin Grutzner, Georg |
| author_facet | Boucher, Kevin Grutzner, Georg |
| contents | We investigate growth properties of cocycles with values in uniformly bounded representations on super-reflexive Banach spaces; this includes $L^p$-spaces for $1<p<\infty$ as well as Hilbert spaces. We then study the generalized Hilbert compression of cocycles arising in this setting for the Property (T) groups $\mathrm{Sp}(n,1)$, $n\ge 2$, and establish the existence of uniformly Lipschitz affine actions with optimal growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06322 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniformly affine actions on Banach spaces: growth of cocycles Boucher, Kevin Grutzner, Georg Group Theory Functional Analysis Representation Theory 22D12, 43A07, 20F69, 22D55 We investigate growth properties of cocycles with values in uniformly bounded representations on super-reflexive Banach spaces; this includes $L^p$-spaces for $1<p<\infty$ as well as Hilbert spaces. We then study the generalized Hilbert compression of cocycles arising in this setting for the Property (T) groups $\mathrm{Sp}(n,1)$, $n\ge 2$, and establish the existence of uniformly Lipschitz affine actions with optimal growth. |
| title | Uniformly affine actions on Banach spaces: growth of cocycles |
| topic | Group Theory Functional Analysis Representation Theory 22D12, 43A07, 20F69, 22D55 |
| url | https://arxiv.org/abs/2601.06322 |