Operator-Lipschitz functions in Schatten-von Neumann classes

Abstract

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

In comparison to the previous version, the whole new section is introduced in order to resolve the continuous case. A number of minor typos are fixed also