Eigenvalues for Some Complex In nite Tridiagonal Matrices

The discrete spectrum for an unbounded operator J dened by a special innite tridiagonal complex matrix is approximated by the eigenvalues of its orthogonal truncations. Let σ(J) means the spectrum of the operator J and here Limn→∞λn is the set of limit points of the sequence (λn); and the n x n matrix Jn is an orthogonal truncation of J. We consider classes of tridiagonal complex matrices for which σ(J) = Λ(J).