On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms

The norm of an integral operator occurring in the partial wave decomposition of an operator <jats:italic>B</jats:italic> introduced by Brown and Ravenhall in a model for relativistic one-electron atoms is determined. The result implies that <jats:italic>B</jats:italic> is non-negative and has no eigenvalue at 0 when the nuclear charge does not exceed a specified critical value.