Operator-Lipschitz functions in Schatten-von Neumann classes
Functional Analysis
2009-12-14 v3 Operator Algebras
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 , . The negative result for , was earlier established by Yu. Farforovskaya in 1972.
Cite
@article{arxiv.0904.4095,
title = {Operator-Lipschitz functions in Schatten-von Neumann classes},
author = {Denis Potapov and Fedor Sukochev},
journal= {arXiv preprint arXiv:0904.4095},
year = {2009}
}
Comments
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