Limit points of eigenvalues of truncated unbounded tridiagonal operators

Central European Journal of Mathematics (Impact Factor: 0.52). 05/2007; 5(2):335-344. DOI: 10.2478/s11533-007-0009-1

ABSTRACT Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e



, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T

. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.

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