On two-isometries in finite-dimensional spaces

Abstract

A linear bounded operator A in a complex Hilbert space H is called a two-isometry if A *2 A 2 - 2A* + 1 = 0. In particular, the class of two-isometries contains conventional isometries. It is shown that in the finite-dimensional case, the notion of two-isometry has no new content, that is, two-isometries of a finite-dimensional unitary space are conventional unitary operators. Bibliography: 3 titles.