, Volume 42, Issue 1, pp 220-224

Unitary similarity of projectors

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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 *.

Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth