Operator-Lipschitz functions in Schatten-von Neumann classes

This paper resolves a number of conjectures in the perturbation theory of linear operators. Namely, we prove that every Lipschitz function is operator Lipschitz in the Schatten-von Neumann ideals $S^{\alpha }$, $1<\alpha <\mathrm{\infty }$. The negative result for $S^{\alpha }$, $\alpha =1,\mathrm{\infty }$ was earlier established by Yu. Farforovskaya in 1972.