当前位置: X-MOL 学术Banach J. Math. Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On Banach space projective tensor product of $$C^*$$C∗-algebras
Banach Journal of Mathematical Analysis ( IF 1.2 ) Pub Date : 2020-01-01 , DOI: 10.1007/s43037-019-00006-4
Ved Prakash Gupta , Ranjana Jain

We analyze certain algebraic structures of the Banach space projective tensor product of $C^*$-algebras which are comparable with their known counterparts or the Haagerup tensor product and the operator space projective tensor product of $C^*$-algebras. Highlights of this analysis include (a) injectivity of the Banach space projective tensor product when restricted to the tensor products of $C^*$-algebras, (b) detailed structure of closed ideals of $A \otimes_{\gamma} B$ in terms of those of $A$ and $B$, (c) identification of certain spaces of ideals of $A \otimes_{\gamma} B$ in terms of those of $A$ and $B$ from the perspective of hull-kernel topology, and (d) identification of the center of $A \otimes_{\gamma} B$ with $Z(A) \otimes_{\gamma} Z(B)$, where $A$ and $B$ are $C^*$-algebras.

中文翻译:

关于 $$C^*$$C∗-代数的 Banach 空间投影张量积

我们分析了 $C^*$-代数的 Banach 空间投影张量积的某些代数结构,它们与已知的对应物或 Haagerup 张量积和 $C^*$-代数的算子空间投影张量积相当。该分析的亮点包括 (a) 当限制为 $C^*$-代数的张量积时,Banach 空间投影张量积的注入性,(b) $A \otimes_{\gamma} B$ 的封闭理想的详细结构就$A$和$B$而言,(c) 从船体的角度识别$A\otimes_{\gamma} B$的某些理想空间。 -内核拓扑结构,以及 (d) 用 $Z(A) \otimes_{\gamma} Z(B)$ 识别 $A \otimes_{\gamma} B$ 的中心,其中 $A$ 和 $B$ 是$C^*$-代数。
更新日期:2020-01-01
down
wechat
bug