2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162574We give an example of an operator with different weak and strong absolutely continuous subspaces, and a counterexample to the duality problem for the spectral components. Both examples are optimal in the scale of compact operators.13 pages; a counterexample to the duality problem for spectral components has been addedFunctional AnalysisMathematical Physics47A65; 47B44text