  The variation of spectral subspaces for linear self-adjoint operators under
an additive bounded semidefinite perturbation is considered. A variant of the
Davis-Kahan $ \sin2\Theta $ theorem from [SIAM J. Numer. Anal. 7 (1970), 1--46]
adapted to this situation is proved. Under a certain additional geometric
assumption on the separation of the spectrum of the unperturbed operator, this
leads to a sharp estimate on the norm of the difference of the spectral
projections associated with isolated components of the spectrum of the
perturbed and unperturbed operators, respectively. Without this additional
geometric assumption on the isolated components of the spectrum of the
unperturbed operator, a corresponding estimate is obtained by transferring the
optimization approach for general perturbations in [J. Anal. Math. 135 (2018),
313--343] to the present situation.
