Criterion for the resolvent set of nonsymmetric tridiagonal operators
  We study nonsymmetric tridiagonal operators acting in the Hilbert space $\ell^2$ and describe the spectrum and the resolvent set of such operators in terms of a continued fraction related to the resolvent. In this way we establish a connection between Pad\'e approximants and spectral properties of nonsymmetric tridiagonal operators. 
A. I. Aptekarev, Valeri\u{\i} A. Kaliaguine, Walter Van Assche