Some sharp norm estimates in the subspace perturbation problem

Details Some sharp norm estimates in the subspace perturbation problem Some sharp norm estimates in the subspace perturbation problem

2004-09-28

arxiv.org/abs/math/0409558v2

Integral Equations and Operator Theory 56 (2006), 511-542

Mathematics

Spectral Theory

Scientific paper

10.1007/s00020-006-1437-1

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 \textit{a priori} sharp bound on variation of the corresponding spectral subspace under off-diagonal perturbations. This bound represents a new, \textit{a priori}, $\tan\Theta$ Theorem. We also extend the Davis--Kahan $\tan 2\Theta$ Theorem to the case of some unbounded perturbations.

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