2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134781We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of the difference of two spectral projections.Spectral TheoryMathematical Physics47A15; 47A55; 47B15text