The essential spectrum of some unbounded Jacobi matrices: A generalization of the Last–Simon approach

Abstract We consider some unbounded Jacobi matrices J with zero main diagonal and off diagonal entries defined by two different rules and calculate their essential spectrum by extending Last and Simon’s ideas from the bounded to the unbounded case. We show that the essential spectrum of J is the union of the spectra of three limit matrices J z , J z c , and J c z . Finally, we give a description of each of these spectra.