Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published December 2017 | Submitted
Journal Article Open

Similarity Between Two Projections

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

Submitted - 1705.08937.pdf

Files

1705.08937.pdf
Files (185.9 kB)
Name Size Download all
md5:025b9e9df5fb619181ba290b4c2c6297
185.9 kB Preview Download

Additional details

Created:
August 21, 2023
Modified:
October 17, 2023