Abstract
An analogue of the Davis-Kahan \({\sin 2\Theta}\) theorem from (SIAM J Numer Anal 7:1–46, 1970) is proved under a general spectral separation condition. This extends the generic \({\sin 2\theta}\) estimates recently shown by Albeverio and Motovilov in (Complex Anal Oper Theory 7:1389–1416, 2013). The result is applied to the subspace perturbation problem to obtain a bound on the arcsine of the norm of the difference of the spectral projections associated with isolated components of the spectrum of the unperturbed and perturbed operators, respectively.
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The material presented in this work will be part of the author’s Ph.D. thesis.
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Seelmann, A. Notes on the \({\sin 2 \Theta}\) Theorem. Integr. Equ. Oper. Theory 79, 579–597 (2014). https://doi.org/10.1007/s00020-014-2127-z
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DOI: https://doi.org/10.1007/s00020-014-2127-z