Geodesic
On two-isometries in finite-dimensional spaces
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 71-74

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A linear bounded operator $A$ in a complex Hilbert space $H$ is called a 2-isometry if $A^{*2}A^2-2A^*A+I=0$. In particular, the class of 2-isometries contains conventional isometries. It is shown that in the finite-dimensional case, the concept of a 2-isometry has no new content, that is, 2-isometries of a finite-dimensional unitary space are conventional unitary operators. 
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     author = {Kh. D. Ikramov},
     title = {On two-isometries in finite-dimensional spaces},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_395_a6/}
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Kh. D. Ikramov. On two-isometries in finite-dimensional spaces. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 71-74. http://geodesic.mathdoc.fr/item/ZNSL_2011_395_a6/