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Published September 1, 2017 | Submitted
Journal Article Open

Unitaries permuting two orthogonal projections

Abstract

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.

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.

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Created:
August 21, 2023
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