On two-isometries in finite-dimensional spaces (Q690605)

From the author's abstract: ``A~linear bounded operator \(A\) in a complex Hilbert space \(H\) is called a two-isometry if \(A^{\ast 2} A^2 - 2A^\ast A+I=0\). In particular, the class of two-isometries contains conventional isometries.'' The author shows that, if a two-isometry operator acts on a complex Hilbert space of dimension \(n\), then it is a conventional unitary operator.