On the Removal of Finite Discrete Spectrum by Coefficient Stripping

Abstract

We prove for a large class of operators, $J$, including block Jacobi matrices, if $\sigma (J)\setminus [\alpha ,\beta ]$ is a finite set, each point of which is an eigenvalue of finite multiplicity, then a finite coefficient stripped, $J_N$, has $\sigma (J_N)\subset [\alpha ,\beta ]$. We use an abstract Dirichlet decoupling.