Limit points of eigenvalues of truncated unbounded tridiagonal operators

ArticleinCentral European Journal of Mathematics 5(2):335-344 · May 2007with7 Reads
Impact Factor: 0.58 · 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

    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.