Abstract.
We discuss the spectral subspace perturbation problem for a self-adjoint operator. Assuming that the convex hull of a part of its spectrum does not intersect the remainder of the spectrum, we establish an a priori sharp bound on variation of the corresponding spectral subspace under off-diagonal perturbations. This bound represents a new, a priori, tan Θ Theorem. We also extend the Davis–Kahan tan 2Θ Theorem to the case of some unbounded perturbations.
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Motovilov, A.K., Selin, A.V. Some Sharp Norm Estimates in the Subspace Perturbation Problem. Integr. equ. oper. theory 56, 511–542 (2006). https://doi.org/10.1007/s00020-006-1437-1
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DOI: https://doi.org/10.1007/s00020-006-1437-1