2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214254We consider a periodic pseudodifferential operator $H=(-Δ)^l+A$ ($l>0$) in $\R^d$ which satisfies the following conditions: (i) the symbol of $H$ is smooth in $x$, and (ii) the perturbation $A$ has order smaller than $2l-1$. Under these assumptions, we prove that the spectrum of $H$ contains a half-line.33 pages; misprints corrected; to appear in CPDESpectral TheoryAnalysis of PDEs35P20 (Primary); 58J40, 58J50, 35J10 (Secondary)text