  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 $S^\alpha$, $1 < \alpha < \infty$.
The negative result for $S^\alpha$, $\alpha = 1, \infty$ was earlier
established by Yu. Farforovskaya in 1972.
