Operator-Lipschitz functions in Schatten-von Neumann classes

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Potapov, Denis
Sukochev, Fedor
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Abstract
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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.
Comment: 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
Keywords
Mathematics - Functional Analysis, Mathematics - Operator Algebras, 47A56, 47B10, 47B47
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