TY - JOUR
T1 - Similarity Between Two Projections
AU - Böttcher, Albrecht
AU - Simon, Barry
AU - Spitkovsky, Ilya
N1 - Publisher Copyright:
© 2017, Springer International Publishing AG, part of Springer Nature.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - 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.
AB - 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.
KW - Intertwining operators
KW - Intertwining unitaries
KW - Similar projections
KW - Two projections
UR - http://www.scopus.com/inward/record.url?scp=85034619183&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85034619183&partnerID=8YFLogxK
U2 - 10.1007/s00020-017-2414-6
DO - 10.1007/s00020-017-2414-6
M3 - Article
AN - SCOPUS:85034619183
SN - 0378-620X
VL - 89
SP - 507
EP - 518
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
IS - 4
ER -