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 *.
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Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth
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Doković, D.Ž. Unitary similarity of projectors. Aeq. Math. 42, 220–224 (1991). https://doi.org/10.1007/BF01818492
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DOI: https://doi.org/10.1007/BF01818492