E.M. Harrell II, P.L. Michel
Commutator Bounds for Eigenvalues, with applications to Spectral Geometry
(37K, Latex)

ABSTRACT.   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.