arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1104.4935math.FAmath.OA
收藏

连续域的Banach和$C^*$ -代数的射影性

Projectivity of Banach and $C^*$-algebras of continuous fields

David Cushing, Zinaida A. Lykova

备注：
34 pages
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

给出了由Banach代数的局部平凡连续域定义的Banach代数左投射和双投射的充要条件。我们证明了由局部平凡连续域$\mathcal{U} = \{Ω,(A_t)_{t \in Ω},Θ\}$定义的投射$C^*$ -代数$\A$，使得每个$C^*$ -代数$ A_{t}$都有严格正元素.对于包含在${\cal B}(H)$中的交换$C^*$ -代数$\D$，其中$H$是可分Hilbert空间，我们证明了$\D$的左投射性条件等价于$\D$中严格正元的存在，从而等价于$\D$的谱是Lindel $\ddot{\rm o}$ f空间.

英文摘要：

We give necessary and sufficient conditions for the left projectivity and biprojectivity of Banach algebras defined by locally trivial continuous fields of Banach algebras. We identify projective $C^*$-algebras $\A$ defined by locally trivial continuous fields $\mathcal{U} = \{Ω,(A_t)_{t \in Ω},Θ\}$ such that each $C^*$-algebra $ A_{t}$ has a strictly positive element. For a commutative $C^*$-algebra $\D$ contained in ${\cal B}(H)$, where $H$ is a separable Hilbert space, we show that the condition of left projectivity of $\D$ is equivalent to the existence of a strictly positive element in $\D$ and so to the spectrum of $\D$ being a Lindel$\ddot{\rm o}$f space.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑