Similarity Between Two Projections
Similarity Between Two Projections
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DOI：
10.1007/s00020-017-2414-6
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发表时间：
2017-05
影响因子：
0.8
通讯作者：
A. Böttcher;B. Simon;I. Spitkovsky
中科院分区：
文献类型：
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作者：
A. Böttcher;B. Simon;I. Spitkovsky
给出两个正交投影PandQ，我们对所有的酉算子感兴趣。这样的单元以前已经由王、杜、窦以及其中一位作者构造过。这篇笔记的目的之一是比较这些结构。就在最近，窦、石、崔、杜四人描述了所有具有所需性质的单位。他们的证明是通过Halmos的两个投影定理得到的。本文基于Avron，Seler和作者之一的超对称方法给出了一个证明。
Given two orthogonal projectionsPandQ, we are interested in all unitary operatorsUsuch thatand. Such unitariesUhave previously been constructed by Wang, Du, and Dou and also by one of the authors. One purpose of this note is to compare these constructions. Very recently, Dou, Shi, Cui, and Du described all unitariesUwith the required property. Their proof is via the two projections theorem by Halmos. We here give a proof based on the supersymmetric approach by Avron, Seiler, and one of the authors.