  Many black-hole sources emit a substantial fraction of their luminosities in
blackbody-like spectral components. It is usual to assume that these are
produced in regions at least comparable in size to the hole's Schwarzschild
radius, so that a measure of the emitting area provides an estimate of the
black hole mass M. However there is then no guarantee that the source
luminosity (if isotropic) obeys the Eddington limit corresponding to M. We show
that the apparent blackbody luminosity L_sph and temperature T must obey the
inequality L_sph < 2.3 10^44 (T/100 eV)^-4 erg s^-1 for this to hold. Sources
violating this limit include ultrasoft AGN and some of the ultraluminous X-ray
sources (ULXs) observed in nearby galaxies. We discuss the possible
consequences of this result, which imply either super-Eddington or anisotropic
emission in both cases. We suggest that the ultrasoft AGN are the AGN analogues
of the ULXs.
