aequationes mathematicae

, Volume 42, Issue 1, pp 220–224

Unitary similarity of projectors

  • Dragomir Ž Doković
Research Papers

Summary

We deal with linear operators acting in a finite dimensional complex Hilbert space. We show that there exists a simple canonical form for projectors (not necessarily orthogonal) under unitary similarity. As a consequence we obtain a simple test for unitary similarity of projectors. IfP is a projector we show thatP andP* are unitarily similar. We also determine the isomorphism type of the algebra generated by the projectorsP andP*.

AMS (1980) subject classification

Primary 15A21, 15A30 Secondary 15A72, 15A18 

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References

  1. [1]
    Bhattacharya, R. andMukherjea, K.,On unitary similarity of matrices, Linear Algebra and its Appl.126 (1989), 95–105.CrossRefGoogle Scholar
  2. [2]
    Herstein, I. N., “Noncommutative Rings”, Carus Math. Monograph No. 15, Math. Assoc. Amer. 1968.Google Scholar
  3. [3]
    Pearcy, C.,A complete set of unitary invariants for operators generating finite W *-algebras of type I, Pacific J. Math.12 (1962), 1405–1414.Google Scholar

Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Dragomir Ž Doković
    • 1
  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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