Published December 2017
| Submitted
Journal Article
Open
Similarity Between Two Projections
Chicago
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Abstract
Given two orthogonal projections P and Q, we are interested in all unitary operators U such that UP=QU and UQ=PU. 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.
Additional Information
© 2017 Springer International Publishing AG, part of Springer Nature. Received: 29 May 2017; Revised: 01 November 2017; First Online: 20 November 2017. Research of the Barry Simon supported in part by NSF Grants DMS-1265592 and DMS-1665526 and in part by Israeli BSF Grant No. 2014337. The Ilya Spitkovsky was supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi.Attached Files
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Additional details
- Eprint ID
- 83396
- Resolver ID
- CaltechAUTHORS:20171121-100155399
- NSF
- DMS-1265592
- NSF
- DMS-1665526
- Binational Science Foundation (USA-Israel)
- 2014337
- New York University Abu Dhabi
- Created
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2017-11-21Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field