Harmonic operators on convolution quantum group algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914800683974656 |
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| author | Nemati, Mehdi Renani, Sima Soltani |
| author_facet | Nemati, Mehdi Renani, Sima Soltani |
| contents | Let ${\Bbb G}$ be a locally compact quantum group and ${\mathcal T}(L^2({\Bbb G}))$ be the Banach algebra of trace class operators on $L^2({\Bbb G})$ with the convolution induced by the right fundamental unitary of ${\Bbb G}$. We study the space of harmonic operators $\widetilde{\mathcal H}_ω$ in ${\mathcal B}(L^2({\Bbb G}))$ associated to a contractive element $ω\in {\mathcal T}(L^2({\Bbb G}))$. We characterize the existence of non-zero harmonic operators in ${\mathcal K}(L^2({\Bbb G}))$ and relate them with some properties of the quantum group ${\Bbb G}$, such as finiteness, amenability and co-amenability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10910 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harmonic operators on convolution quantum group algebras Nemati, Mehdi Renani, Sima Soltani Operator Algebras Functional Analysis 22D15, 43A07, 43A22, 46H05 Let ${\Bbb G}$ be a locally compact quantum group and ${\mathcal T}(L^2({\Bbb G}))$ be the Banach algebra of trace class operators on $L^2({\Bbb G})$ with the convolution induced by the right fundamental unitary of ${\Bbb G}$. We study the space of harmonic operators $\widetilde{\mathcal H}_ω$ in ${\mathcal B}(L^2({\Bbb G}))$ associated to a contractive element $ω\in {\mathcal T}(L^2({\Bbb G}))$. We characterize the existence of non-zero harmonic operators in ${\mathcal K}(L^2({\Bbb G}))$ and relate them with some properties of the quantum group ${\Bbb G}$, such as finiteness, amenability and co-amenability. |
| title | Harmonic operators on convolution quantum group algebras |
| topic | Operator Algebras Functional Analysis 22D15, 43A07, 43A22, 46H05 |
| url | https://arxiv.org/abs/2405.10910 |