On low-dimensional partial isometries

Published 5 Jun 2022 in math.FA | (2206.02141v1)

Abstract: Two statements concerning $n$-by-$n$ partial isometries are being considered: (i) these matrices are generic, if unitarily irreducible, and (ii) if nilpotent, their numerical ranges are circular disks. Both statements hold for $n\leq 4$ but fail starting with $n=5$.

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