Similarity Between Two Projections

Similarity Between Two Projections Given two orthogonal projections P and Q, we are interested in all unitary operators U such that $$UP=QU$$ U P = Q U and $$UQ=PU$$ U Q = P U . Such unitaries U have 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 unitaries U with 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Integral Equations and Operator Theory Springer Journals
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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis
ISSN
0378-620X
eISSN
1420-8989
D.O.I.
10.1007/s00020-017-2414-6
Publisher site
See Article on Publisher Site

Abstract

Given two orthogonal projections P and Q, we are interested in all unitary operators U such that $$UP=QU$$ U P = Q U and $$UQ=PU$$ U Q = P U . Such unitaries U have 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 unitaries U with 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.

Journal

Integral Equations and Operator TheorySpringer Journals

Published: Nov 20, 2017

References

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