Rigidity of pseudofunction algebras of ample groupoids
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911000123408384 |
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| author | Gardella, Eusebio Palmstrøm, Mathias Thiel, Hannes |
| author_facet | Gardella, Eusebio Palmstrøm, Mathias Thiel, Hannes |
| contents | We show that a Hausdorff, ample groupoid $\mathcal{G}$ can be completely recovered from the $I$-norm completion of $C_c(\mathcal{G})$. More generally, we show that this is also the case for the algebra of symmetrized $p$-pseudofunctions, as well as for the reduced groupoid $L^p$-operator algebra, for $p\neq 2$.
Our proofs are based on a new construction of an inverse semigroup built from Moore-Penrose invertible partial isometries in an $L^p$-operator algebra. Along the way, we verify a conjecture of Rakočević concerning the continuity of the Moore-Penrose inverse for $L^p$-operator algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of pseudofunction algebras of ample groupoids Gardella, Eusebio Palmstrøm, Mathias Thiel, Hannes Operator Algebras Dynamical Systems Group Theory Primary 47L10, Secondary 46L55, 20M18 We show that a Hausdorff, ample groupoid $\mathcal{G}$ can be completely recovered from the $I$-norm completion of $C_c(\mathcal{G})$. More generally, we show that this is also the case for the algebra of symmetrized $p$-pseudofunctions, as well as for the reduced groupoid $L^p$-operator algebra, for $p\neq 2$. Our proofs are based on a new construction of an inverse semigroup built from Moore-Penrose invertible partial isometries in an $L^p$-operator algebra. Along the way, we verify a conjecture of Rakočević concerning the continuity of the Moore-Penrose inverse for $L^p$-operator algebras. |
| title | Rigidity of pseudofunction algebras of ample groupoids |
| topic | Operator Algebras Dynamical Systems Group Theory Primary 47L10, Secondary 46L55, 20M18 |
| url | https://arxiv.org/abs/2506.09563 |