Commutator Bounds for Eigenvalues, with Applications to Spectral Geometry
Harrell, Evans M., II
Michel, Patricia L.
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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.