Burenkov V.I., Evans W.D. On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms (27K, LATEX) ABSTRACT. The norm of an integral operator occurring in the partial wave decomposition of an operator $B$ introduced by Brown and Ravenhall in a model for relativistic one-electron atoms is determined. The result implies that $B$ is non-negative and has no eigenvalue at $0$ when the nuclear charge does not exceed a specified critical value.