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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 α , 1 < α < ∞. The negative result for S α , α = 1, ∞ was earlier established by Yu. Farforovskaya in 1972. Alternatively, for every 1 < α < ∞, there is a(More)
Suppose that f is a Lipschitz function on R with f Lip ≤ 1. Let A be a bounded self-adjoint operator on a Hilbert space H. Let p ∈ (1, ∞) and suppose that x ∈ B(H) is an operator such that the commutator [A, x] is contained in the Schatten class S p. It is proved by the last two authors, that then also [f (A), x] ∈ S p and there exists a constant C p(More)
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