Topological stable rank of nest algebras
Topological stable rank of nest algebras
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DOI：
10.1112/plms/pdn048
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发表时间：
2008-04
影响因子：
1.8
通讯作者：
K. Davidson;Y. Ji
中科院分区：
文献类型：
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作者：
K. Davidson;Y. Ji
我们建立了关于将巴纳赫代数上的右可逆行扩展到可逆矩阵的一般结果。这应用于分裂精确序列的右拓扑稳定秩的计算。我们还引入了稳定排名的定量衡量标准。这些结果用于计算所有嵌套代数的右（左）拓扑稳定等级。该值为 2 或无穷大，并且仅当 𝒩 为小于 ω2 的序数类型且原子尺寸增长得足够快时，才会出现 rtsr (𝒯(𝒩)) = 2。我们介绍巴纳赫代数上“部分矩阵代数”的一般结果。这用于获得类似于巴纳赫代数上的矩阵代数的 Rieffel 公式的不等式。这用于进一步了解巢箱。
We establish a general result about extending a right invertible row over a Banach algebra to an invertible matrix. This is applied to the computation of right topological stable rank of a split exact sequence. We also introduce a quantitative measure of stable rank. These results are applied to compute the right (left) topological stable rank for all nest algebras. This value is either 2 or infinity, and rtsr (𝒯(𝒩)) = 2 occurs only when 𝒩 is of ordinal type less than ω2 and the dimensions of the atoms grows sufficiently quickly. We introduce general results on ‘partial matrix algebras’ over a Banach algebra. This is used to obtain an inequality akin to Rieffel's formula for matrix algebras over a Banach algebra. This is used to give further insight into the nest case.