On generators of abelian Kadison–Singer algebras in matrix algebras
On generators of abelian Kadison–Singer algebras in matrix algebras
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DOI：
10.1016/j.laa.2013.10.031
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发表时间：
2014
影响因子：
1.1
通讯作者：
Wenming Wu;Wei Yuan
中科院分区：
文献类型：
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作者：
Wenming Wu;Wei Yuan
假设H是一个维数大于2的希尔伯特空间。证明了作用在H上的交换Kadison-Singer代数不可能包含任何非平凡幂等元。在此基础上，证明了矩阵代数Mn（C）（n <$3）中的交换KS-代数不能由单个元素生成.作为推论，还证明了交换KS-代数的格不可能是完全分配的。
Assume that H is a Hilbert space of dimension greater than two. We prove that an abelian Kadison–Singer algebra acting on H cannot contain any non-trivial idempotent. Based on this, we show that an abelian KS-algebra in matrix algebra M n (C)(n⩾ 3) cannot be generated by a single element. As a corollary, it is also proved that the lattice of an abelian KS-algebra cannot be completely distributive.