Some Sharp Norm Estimates in the Subspace Perturbation Problem |
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Authors: | Alexander K. Motovilov Alexei V. Selin |
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Affiliation: | (1) Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia;(2) Laboratory of Informational Technologies, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia |
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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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Keywords: | Primary 47A55 Secondary 47B25 |
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