The essential spectrum of Schrodinger, Jacobi, and CMV operators
  We provide a very general result that identifies the essential spectrum of broad classes of operators as exactly equal to the closure of the union of the spectra of suitable limits at infinity. Included is a new result on the essential spectra when potentials are asymptotic to isospectral tori. We also recover with a unified framework the HVZ theorem and Krein's results on orthogonal polynomials with finite essential spectra. 
Yoram Last, Barry Simon