Abstract
This paper resolves a number of problems in the perturbation theory of linear operators, linked with the 45-year-old conjecure of M. G. Kreĭn. In particular, we prove that every Lipschitz function is operator-Lipschitz in the Schatten–von Neumann ideals S α, 1 < α < ∞. Alternatively, for every 1 < α < ∞, there is a constant c α > 0 such that
where f is a Lipschitz function with
\( {\left\| \cdot \right\|_{\alpha }} \) is the norm is S α, and a and b are self-adjoint linear operators such that \( a - b \in {S^{\alpha }} \).
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2000 Math. Subject Classification: 47A56, 47B10, 47B47.
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Potapov, D., Sukochev, F. Operator-Lipschitz functions in Schatten–von Neumann classes. Acta Math 207, 375–389 (2011). https://doi.org/10.1007/s11511-012-0072-8
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DOI: https://doi.org/10.1007/s11511-012-0072-8