On permanence of regularity properties II
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915843052404736 |
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| author | Lee, Hyun Ho |
| author_facet | Lee, Hyun Ho |
| contents | In this article, we study the permanence of topological and algebraic dimension type properties of simple unital $C\sp*$-algebras. When a pair of unital $C\sp*$-algebras $(A, B)$ is associated by a $*$-homomorphism $ϕ: A\to B$ which is tracially sequentially-split by order zero, we show that under suitable assumptions on either $A$ or $B$, or both $A$ and $B$ \begin{itemize} \item tracial $m$-comparison passes from $B$ to $A$; \item tracial $m$-almost divisibility passes from $B$ to $A$; \item tracial nuclear dimension less than $m$ passes from $B$ to $A$. \end{itemize} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07491 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On permanence of regularity properties II Lee, Hyun Ho Operator Algebras Primary:46L55 Secondary: 47C15, 46L35 In this article, we study the permanence of topological and algebraic dimension type properties of simple unital $C\sp*$-algebras. When a pair of unital $C\sp*$-algebras $(A, B)$ is associated by a $*$-homomorphism $ϕ: A\to B$ which is tracially sequentially-split by order zero, we show that under suitable assumptions on either $A$ or $B$, or both $A$ and $B$ \begin{itemize} \item tracial $m$-comparison passes from $B$ to $A$; \item tracial $m$-almost divisibility passes from $B$ to $A$; \item tracial nuclear dimension less than $m$ passes from $B$ to $A$. \end{itemize} |
| title | On permanence of regularity properties II |
| topic | Operator Algebras Primary:46L55 Secondary: 47C15, 46L35 |
| url | https://arxiv.org/abs/2603.07491 |