Criterion for the resolvent set of nonsymmetric tridiagonal operators

Aptekarev, A. I.; Kaliaguine, V.; Van Assche, W.

doi:10.1090/S0002-9939-1995-1254830-5

Criterion for the resolvent set of nonsymmetric tridiagonal operators
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by A. I. Aptekarev, V. Kaliaguine and W. Van Assche

Proc. Amer. Math. Soc. 123 (1995), 2423-2430

DOI: https://doi.org/10.1090/S0002-9939-1995-1254830-5

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Abstract:

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 Padé approximants and spectral properties of nonsymmetric tridiagonal operators.

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