Strict comparison holds in the uniform Roe algebra of a discrete amenable group
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918477857554432 |
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| author | Elliott, George A. Li, Chun Guang Niu, Zhuang Zhang, Jianguo |
| author_facet | Elliott, George A. Li, Chun Guang Niu, Zhuang Zhang, Jianguo |
| contents | Let $Γ$ be a countable discrete amenable group, and let $A=l^\infty(Γ) \rtimes Γ$ or $A = \mathrm{C}(M) \rtimes Γ$, where $(M, Γ)$ is the universal minimal set of $Γ$. It is shown that if $a, b \in A \otimes \mathcal K$ are positive elements such that $$\mathrm{d}_τ(a) < \mathrm{d}_τ(b),\quad τ\in \mathrm{T}(A),$$ then $a$ is Cuntz subequivalent to $b$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01053 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strict comparison holds in the uniform Roe algebra of a discrete amenable group Elliott, George A. Li, Chun Guang Niu, Zhuang Zhang, Jianguo Operator Algebras Dynamical Systems Let $Γ$ be a countable discrete amenable group, and let $A=l^\infty(Γ) \rtimes Γ$ or $A = \mathrm{C}(M) \rtimes Γ$, where $(M, Γ)$ is the universal minimal set of $Γ$. It is shown that if $a, b \in A \otimes \mathcal K$ are positive elements such that $$\mathrm{d}_τ(a) < \mathrm{d}_τ(b),\quad τ\in \mathrm{T}(A),$$ then $a$ is Cuntz subequivalent to $b$. |
| title | Strict comparison holds in the uniform Roe algebra of a discrete amenable group |
| topic | Operator Algebras Dynamical Systems |
| url | https://arxiv.org/abs/2605.01053 |