Twisted crossed products of Banach algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916023235510272 |
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| author | Delfín, Alonso Farsi, Carla Packer, Judith |
| author_facet | Delfín, Alonso Farsi, Carla Packer, Judith |
| contents | Given a locally compact group $G$, a nondegenerate Banach algebra $A$ with a contractive approximate identity, a twisted action $(α, σ)$ of $G$ on $A$, and a family $\mathcal{R}$ of uniformly bounded representations of $A$ on Banach spaces, we define the twisted crossed product $F_\mathcal{R}(G,A,α, σ)$. When $\mathcal{R}$ consists of contractive representations, we show that $F_\mathcal{R}(G,A,α, σ)$ is a Banach algebra with a contractive approximate identity, which can also be characterized by an isometric universal property.
As an application, we specialize to the $L^p$-operator algebra setting, defining both the $L^p$-twisted crossed product and the reduced version. Finally, we give a generalization of the so-called Packer-Raeburn trick to the $L^p$-setting, showing that any $L^p$-twisted crossed product is "stably" isometrically isomorphic to an untwisted one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted crossed products of Banach algebras Delfín, Alonso Farsi, Carla Packer, Judith Functional Analysis Dynamical Systems Operator Algebras Primary 46H05, 46H15, 46H35, 47L65, Secondary 43A15, 43A20, 47L10 Given a locally compact group $G$, a nondegenerate Banach algebra $A$ with a contractive approximate identity, a twisted action $(α, σ)$ of $G$ on $A$, and a family $\mathcal{R}$ of uniformly bounded representations of $A$ on Banach spaces, we define the twisted crossed product $F_\mathcal{R}(G,A,α, σ)$. When $\mathcal{R}$ consists of contractive representations, we show that $F_\mathcal{R}(G,A,α, σ)$ is a Banach algebra with a contractive approximate identity, which can also be characterized by an isometric universal property. As an application, we specialize to the $L^p$-operator algebra setting, defining both the $L^p$-twisted crossed product and the reduced version. Finally, we give a generalization of the so-called Packer-Raeburn trick to the $L^p$-setting, showing that any $L^p$-twisted crossed product is "stably" isometrically isomorphic to an untwisted one. |
| title | Twisted crossed products of Banach algebras |
| topic | Functional Analysis Dynamical Systems Operator Algebras Primary 46H05, 46H15, 46H35, 47L65, Secondary 43A15, 43A20, 47L10 |
| url | https://arxiv.org/abs/2509.24106 |