On the continuity of derivations over locally regular Banach algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915850855907328 |
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| author | Flores, Felipe I. |
| author_facet | Flores, Felipe I. |
| contents | We study the problem of continuity of derivations over Banach algebras. More specifically, we consider a class of Banach algebras that contain a dense '$C^*$-like' subalgebra. We discuss applications to $L^p$-crossed products and symmetrized $L^p$-crossed products. As an example, our results imply that every derivation over the $L^p$-crossed product $F^p(G,X,α)$ is continuous, provided that $G$ is infinite, finitely generated, has polynomial growth, and acts freely on the compact Hausdorff space $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the continuity of derivations over locally regular Banach algebras Flores, Felipe I. Functional Analysis Operator Algebras Primary 46H40, Secondary 46H05, 43A15 We study the problem of continuity of derivations over Banach algebras. More specifically, we consider a class of Banach algebras that contain a dense '$C^*$-like' subalgebra. We discuss applications to $L^p$-crossed products and symmetrized $L^p$-crossed products. As an example, our results imply that every derivation over the $L^p$-crossed product $F^p(G,X,α)$ is continuous, provided that $G$ is infinite, finitely generated, has polynomial growth, and acts freely on the compact Hausdorff space $X$. |
| title | On the continuity of derivations over locally regular Banach algebras |
| topic | Functional Analysis Operator Algebras Primary 46H40, Secondary 46H05, 43A15 |
| url | https://arxiv.org/abs/2507.23696 |