%0 Journal Article
%T Notes on the sin2жи theorem
%A Albrecht Seelmann
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s00020-014-2127-z
%X An analogue of the Davis-Kahan sin2\Theta\ theorem from [SIAM J. Numer. Anal. 7 (1970), 1--46] is proved under a general spectral separation condition. This extends the generic sin2\theta\ 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.
%U http://arxiv.org/abs/1310.2036v1