C. Tix Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall (24K, LaTeX2e) ABSTRACT. We prove that the spectrum of a suitably projected Dirac operator - sometimes called no-pair operator -- introduced by Brown and Ravenhall is bounded from below by some positive constant when the nuclear charge is below some critical charge. This bound improves a result obtained recently by Evans et al and disproves a conjecture made by Hardekopf and Sucher.