Similarity Between Two Projections

Albrecht Böttcher, Barry Simon, Ilya Spitkovsky

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)507-518
Number of pages12
JournalIntegral Equations and Operator Theory
Volume89
Issue number4
DOIs
StatePublished - Dec 1 2017

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Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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