Fourier coefficients and rapid decay in reduced groupoid C*-algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909419188518912 |
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| author | Fuller, Adam H. Karmakar, Pradyut |
| author_facet | Fuller, Adam H. Karmakar, Pradyut |
| contents | Let $Σ\rightarrow G$ be a twist over a locally compact Hausdorff étale groupoid $G$. Given $f$ in the reduced C$^*$-algebra $C_r^*(Σ;G)$ with open support $U \subseteq G$ we ask when $f$ lies in the closure of the compactly supported sections on $U$. Suppose $G$ satisfies the rapid decay property with respect to a length function $L$. We give a positive answer to our question in two instances: when $L$ is conditionally negative-definite, and when $L$ is the square-root of a locally negative type function on $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourier coefficients and rapid decay in reduced groupoid C*-algebras Fuller, Adam H. Karmakar, Pradyut Operator Algebras Let $Σ\rightarrow G$ be a twist over a locally compact Hausdorff étale groupoid $G$. Given $f$ in the reduced C$^*$-algebra $C_r^*(Σ;G)$ with open support $U \subseteq G$ we ask when $f$ lies in the closure of the compactly supported sections on $U$. Suppose $G$ satisfies the rapid decay property with respect to a length function $L$. We give a positive answer to our question in two instances: when $L$ is conditionally negative-definite, and when $L$ is the square-root of a locally negative type function on $G$. |
| title | Fourier coefficients and rapid decay in reduced groupoid C*-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2412.05410 |