A new class of Kadison–Singer algebras
A new class of Kadison–Singer algebras
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DOI：
10.1016/j.exmath.2010.08.001
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发表时间：
2011
影响因子：
0.7
通讯作者：
Liguang Wang;Wei Yuan
中科院分区：
文献类型：
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作者：
Liguang Wang;Wei Yuan
证明了在可分无限维Hilbert空间中由极大套和一阶投影生成的投影格一般是自反的。此外，我们还证明了相应的自反代数具有极大三角性质，等价地，它是Kadison-Singer代数。对于有限套和有限因子投影生成的格子，也得到了类似的结果。
We show that the projection lattice generated by a maximal nest and a rank one projection in a separable infinite-dimensional Hilbert space is in general reflexive. Moreover we show that the corresponding reflexive algebra has a maximal triangular property, equivalently, it is a Kadison–Singer algebra. Similar results are also obtained for the lattice generated by a finite nest and a projection in a finite factor.