Abstract. General criteria of discreteness of the spectrum for operators associated to positive and unbounded Jacobi matrices are established. These criteria unify well-known previous results on compactness of the resolvent of the above matrices.

AMS Subject Classification (1991): 47A55, 47A75

Keyword(s): Spectral theory, compact resolvent, Jacobi matrices

Received November 25, 2006, and in revised from March 14, 2007. (Registered under 6455/2009.)