MPEJ Volume 14, No. 2, 23 pp. Received: Oct 4, 2006. Revised: Oct 19, 2007. Accepted: Aug 8, 2008. D. H. Jakubassa-Amundsen On the essential spectrum of the Jansen-Hess operator for two-electron ions ABSTRACT: Based on the HVZ theorem, the absence of embedded single-particle eigenvalues and dilation analyticity of the pseudorelativistic no-pair Jansen-Hess operator, it is proven that for subcritical central charge $Z$ there is no singular continuous spectrum in ${\Bbb R} \backslash [\Sigma_0,2m]$. Moreover, for the two-particle Brown-Ravenhall operator, the absence of eigenvalues above $2m$ is shown (if $Z\leq 50$). http://www.maia.ub.es/mpej/Vol/14/2.ps http://www.maia.ub.es/mpej/Vol/14/2.pdf http://www.ma.utexas.edu/mpej/Vol/14/2.ps http://www.ma.utexas.edu/mpej/Vol/14/2.pdf http://mpej.unige.ch/mpej/Vol/14/2.ps http://mpej.unige.ch/mpej/Vol/14/2.pdf