English

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 SαS^\alpha, 1<α<1 < \alpha < \infty. The negative result for SαS^\alpha, α=1,\alpha = 1, \infty 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

R2 v1 2026-06-21T12:55:15.908Z