On Harrell-Stubbe Type Inequalities for the Discrete Spectrum of a Self-Adjoint Operator

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145003We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' versions of their theorems. We also analyze the strength of the various inequalities that ensue. The results contain classical bounds for the eigenvalues. Extensions of a variety of inequalities à la Harrell-Stubbe are illustrated for both geometric and physical problems.42 pagesSpectral TheoryDifferential Geometry35P15; 47A75; 49R50; 58J50On Harrell-Stubbe Type Inequalities for the Discrete Spectrum of a Self-Adjoint Operatortext