Operator-Lipschitz functions in Schatten-von Neumann classes

2009/04/27 by Denis Potapov, Fedor Sukochev, Potapov, Denis +1 · 5 citations
Mathematics · #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.0904.4095

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

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