  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.
