تقرير
$p$-nuclearity of $L^p$-operator crossed products
| العنوان: | $p$-nuclearity of $L^p$-operator crossed products |
|---|---|
| المؤلفون: | Wang, Zhen, Zhu, Sen |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, Mathematics - Operator Algebras |
| الوصف: | Let $(X,\mathcal{B},\mu)$ be a measure space and $A$ be a closed subalgebra of $\mathcal{B}(L^p(X,\mu))$, where $p\in [1,\infty)\setminus\{2\}$. Let $(G,A,\alpha)$ be an $L^p$-operator dynamical system, where $G$ is a countable discrete amenable group. We prove that the full $L^p$-operator crossed product $F^p(G,A,\alpha)$ is $p$-nuclear if and only if $A$ is $p$-nuclear {provided the action} $\alpha$ of $G$ on $A$ is $p$-completely isometric. As applications, we show that $L^p$-Cuntz algebras and $L^p$-irrational rotation algebras are both $p$-nuclear for $p\in [1,\infty)\setminus\{2\}$. Our results solve the {$p$-nuclearity problem} for $L^p$-Cuntz algebras raised by N. C. Phillips. Comment: 19 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.03933 |
| رقم الأكسشن: | edsarx.2305.03933 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |