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Unitaries permuting two orthogonal projections

Simon, Barry (2017) Unitaries permuting two orthogonal projections. Linear Algebra and its Applications, 528 . pp. 436-441. ISSN 0024-3795.

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Let P and Q be two orthogonal projections on a separable Hilbert space, H. Wang, Du and Dou proved that there exists a unitary, U, with UPU^(−1) =Q, UQU^(−1) =P if and only if dim⁡(ker⁡P∩ker⁡(1−Q))=dim⁡(ker⁡Q∩ker⁡(1−P)) (both may be infinite). We provide a new proof using the supersymmetric machinery of Avron, Seiler and Simon.

Item Type:Article
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URLURL TypeDescription Paper
Simon, Barry0000-0003-2561-8539
Additional Information:© 2017 Elsevier Inc. Received 15 March 2017, Accepted 27 March 2017, Available online 29 March 2017. Submitted by P. Semrl. Research supported in part by NSF grant DMS-1265592 and in part by Israeli BSF Grant No. 2010348.
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)2010348
Subject Keywords:Pairs of projections; Index
Classification Code:MSC: 47A05; 47A46; 47A53
Record Number:CaltechAUTHORS:20170509-073922440
Persistent URL:
Official Citation:Barry Simon, Unitaries permuting two orthogonal projections, Linear Algebra and its Applications, Volume 528, 1 September 2017, Pages 436-441, ISSN 0024-3795, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77282
Deposited By: Ruth Sustaita
Deposited On:09 May 2017 20:59
Last Modified:28 Jun 2017 18:14

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