Self-Adjoint Perturbations of Left (Right) Weyl Spectrum for Upper Triangular Operator Matrices

Abstract

Let H be a separable infinite-dimensional Hilbert space. Given the operators (formula presented) is a self-adjoint operator. In this paper, a necessary and sufficient condition is given for MX to be a left (right) Weyl operator for some X ∈ S(H). Moreover, it is shown that(formula presented) where σ∗ is the left (right) Weyl spectrum. Finally, we further characterize the perturbation of the left (right) Weyl spectrum for Hamiltonian operators.