Some sharp norm estimates in the subspace perturbation problem

Alexander K. Motovilov; Alexei V. Selin

doi:10.1007/s00020-006-1437-1

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Some sharp norm estimates in the subspace perturbation problem

Alexander K. Motovilov·Alexei V. Selin

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

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BibTeX RIS

Alexander K. Motovilov, Alexei V. Selin. 2006-04-08. Some sharp norm estimates in the subspace perturbation problem. https://doi.org/10.1007/s00020-006-1437-1

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