, Volume 5, Issue 2, pp 335-344

Limit points of eigenvalues of truncated unbounded tridiagonal operators

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Abstract

Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e n } n=1 , 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 N . 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.