Property $\mathrm{(TTT)}$ and the Cowling--Haagerup constant
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910639937552384 |
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| author | Vergara, Ignacio |
| author_facet | Vergara, Ignacio |
| contents | We show that Property $\mathrm{(TTT)}$ is an obstruction to weak amenability with Cowling--Haagerup constant $1$. More precisely, if $G$ is a countable group and $H$ is an infinite subgroup of $G$ such that the pair $(G,H)$ has relative Property $\mathrm{(TTT)}$, then the weak Haagerup constant $\boldsymbolΛ_{\mathrm{WH}}(G)$ is strictly greater than $1$. We apply this result to some semidirect products and lattices in higher rank algebraic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Property $\mathrm{(TTT)}$ and the Cowling--Haagerup constant Vergara, Ignacio Group Theory Functional Analysis Operator Algebras We show that Property $\mathrm{(TTT)}$ is an obstruction to weak amenability with Cowling--Haagerup constant $1$. More precisely, if $G$ is a countable group and $H$ is an infinite subgroup of $G$ such that the pair $(G,H)$ has relative Property $\mathrm{(TTT)}$, then the weak Haagerup constant $\boldsymbolΛ_{\mathrm{WH}}(G)$ is strictly greater than $1$. We apply this result to some semidirect products and lattices in higher rank algebraic groups. |
| title | Property $\mathrm{(TTT)}$ and the Cowling--Haagerup constant |
| topic | Group Theory Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2404.00433 |