Twisted convolution algebras with coefficients in a differential subalgebra
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913735015137280 |
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| author | Flores, Felipe I. |
| author_facet | Flores, Felipe I. |
| contents | Let $({\sf G},α, ω,\mathfrak B)$ be a measurable twisted action of the locally compact group ${\sf G}$ on a Banach $^*$-algebra $\mathfrak B$ and $\mathfrak A$ a differential Banach $^*$-subalgebra of $\mathfrak B$, which is stable under said action. We observe that $L^1_{α,ω}({\sf G},\mathfrak A)$ is a differential subalgebra of $L^1_{α,ω}({\sf G},\mathfrak B)$. We use this fact to provide new examples of groups with symmetric Banach $^*$-algebras. In particular, we prove that discrete rigidly symmetric extensions of compact groups are symmetric or that semidirect products ${\sf K}\rtimes{\sf H}$, with ${\sf H}$ symmetric and ${\sf K}$ compact, are symmetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08846 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Twisted convolution algebras with coefficients in a differential subalgebra Flores, Felipe I. Operator Algebras Primary 43A20, Secondary 47L65, 47L30 Let $({\sf G},α, ω,\mathfrak B)$ be a measurable twisted action of the locally compact group ${\sf G}$ on a Banach $^*$-algebra $\mathfrak B$ and $\mathfrak A$ a differential Banach $^*$-subalgebra of $\mathfrak B$, which is stable under said action. We observe that $L^1_{α,ω}({\sf G},\mathfrak A)$ is a differential subalgebra of $L^1_{α,ω}({\sf G},\mathfrak B)$. We use this fact to provide new examples of groups with symmetric Banach $^*$-algebras. In particular, we prove that discrete rigidly symmetric extensions of compact groups are symmetric or that semidirect products ${\sf K}\rtimes{\sf H}$, with ${\sf H}$ symmetric and ${\sf K}$ compact, are symmetric. |
| title | Twisted convolution algebras with coefficients in a differential subalgebra |
| topic | Operator Algebras Primary 43A20, Secondary 47L65, 47L30 |
| url | https://arxiv.org/abs/2309.08846 |