Commutator bounds for eigenvalues, with applications to spectralgeometry
Evans M. Harrell, Patricia L. Michel · Communications in Partial Differential Equations · 1994
We prove a purely algebraic version of an eigenvalue inequality of Hile and Protter, and derive corollaries bounding differences of eigenvalues of Laplace– Beltrami operators on manifolds. We significantly improve earlier bounds of Yang and Yau, Li, and Harrell.