Property (T) for Banach algebras
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914919875608576 |
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| author | Elkiær, Emilie Mai Pooya, Sanaz |
| author_facet | Elkiær, Emilie Mai Pooya, Sanaz |
| contents | We define and study the notion of property $(\rm T)$ for Banach algebras, generalizing the one from $C^*$-algebras. For a second countable locally compact group $G$ and a given family of Banach spaces $\mathcal E$, we prove that our Banach algebraic property $(\rm{T}_{\mathcal E})$ of the symmetrized pseudofunction algebras $F^*_{\mathcal E}(G)$ characterizes the Banach property $(\rm{T}_{\mathcal E})$ of Bader, Furman, Gelander and Monod for groups. In case $G$ is a discrete group and $\mathcal E$ is the class of $L^p$-spaces for $1\leq p < \infty$, we also achieve the analogue characterization using the symmetrized $p$-pseudofunction algebras $F^*_{λ_ p}(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18136 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Property (T) for Banach algebras Elkiær, Emilie Mai Pooya, Sanaz Functional Analysis Group Theory Operator Algebras We define and study the notion of property $(\rm T)$ for Banach algebras, generalizing the one from $C^*$-algebras. For a second countable locally compact group $G$ and a given family of Banach spaces $\mathcal E$, we prove that our Banach algebraic property $(\rm{T}_{\mathcal E})$ of the symmetrized pseudofunction algebras $F^*_{\mathcal E}(G)$ characterizes the Banach property $(\rm{T}_{\mathcal E})$ of Bader, Furman, Gelander and Monod for groups. In case $G$ is a discrete group and $\mathcal E$ is the class of $L^p$-spaces for $1\leq p < \infty$, we also achieve the analogue characterization using the symmetrized $p$-pseudofunction algebras $F^*_{λ_ p}(G)$. |
| title | Property (T) for Banach algebras |
| topic | Functional Analysis Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2310.18136 |