Similarity Between Two Projections

Albrecht Böttcher, Barry Simon, Ilya Spitkovsky

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)507-518
Number of pages12
JournalIntegral Equations and Operator Theory
Issue number4
StatePublished - Dec 1 2017


  • Intertwining operators
  • Intertwining unitaries
  • Similar projections
  • Two projections

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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