(1) Department of Mathematics, University of Patras, 26500 Patras, Greece
Abstract:
Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {en} 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 TN. 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.