On the operator Lipschitz norm of the functions $z^n$ on a finite set of the unit circle

The paper contains some remarks concerning of the behavior of the operator Lipschitz norm of the functions $z^n$ on subsets of the unit circle. In particular, we prove that the operator Lipschitz norm of the restriction $z^n$ on a subset $\Lambda$ of the unit circle is equal to $|n|$ if and only if $\Lambda$ contains at least $2|n|$ elements.