Notes on the sin2Θ theorem

Albrecht Seelmann

doi:10.1007/s00020-014-2127-z

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arXiv · 1310.2036

Notes on the sin2Θ theorem

Albrecht Seelmann

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Abstract

An analogue of the Davis-Kahan sin2Θ theorem from [SIAM J. Numer. Anal. 7 (1970), 1--46] is proved under a general spectral separation condition. This extends the generic sin2θ estimates recently shown by Albeverio and Motovilov in [Complex Anal. Oper. Theory 7 (2013), 1389--1416]. 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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Albrecht Seelmann. 2013-10-08. Notes on the sin2Θ theorem. https://doi.org/10.1007/s00020-014-2127-z

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