On products of some unitary operators

N.V. Kalashnіkova

doi:10.15421/241110

On products of some unitary operators

N.V. Kalashnіkova (Oles Honchar Dnipropetrovsk National University)

Abstract

We found a set of values $$$\gamma \in \mathbb{C}$$$, for which the equation $$$U_1 U_2 U_3 = \gamma I$$$ with the conditions $$$U_1^n = U_2^2 = U_3^2 = I$$$ has a solution in the set of unitary operators. It is proved that for any $$$\gamma \in \mathbb{C}$$$, $$$|\gamma| = 1$$$, the operator $$$\gamma I$$$ can be represented as the product of four unitary self-adjoint operators.

Keywords

the unitary operator; self-adjoint operator; eigenvalue of a linear operator

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References

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