Research Papers

aequationes mathematicae

, Volume 42, Issue 1, pp 220-224

First online:

Unitary similarity of projectors

  • Dragomir Ž DokovićAffiliated withDepartment of Pure Mathematics, University of Waterloo

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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