  There are extremely luminous quasi stellar objects (QSOs) at high redshift
which are absent at low redshift. The lower luminosities at low redshifts can
be understood as the external manifestation of either a lower Eddington ratio
or a lower mass. To distinguish between both effects, we determine the possible
dependence of masses and Eddington ratios of QSOs with a fixed luminosity as a
function of redshifts; this avoids the Malmquist bias or any other selection
effect. For the masses and Eddington ratios derived for a sample of QSOs in the
Sloan Digital Sky Survey, we model their evolution by a double linear fit
separating the dependence on redshifts and luminosities. The validity of the
fits and possible systematic effects were tested by the use of different
estimators of masses or bolometric luminosities, and possible intergalactic
extinction effects. The results do not show any significant evolution of black
hole masses or Eddington ratios for equal luminosity QSOs. The black hole mass
only depends on the bolometric luminosity without significant dependence on the
redshift as M_{BH}(10^9 M_sun) = 3.4[L_{bol}(10^{47} erg/s})]^{0.65} on average
for z<5. This must not be confused with the possible evolution in the formation
of black holes in QSOs. The variations of environment might influence the
formation of the black holes but not its subsequent accretion. It also leaves a
question to be solved: Why are there not QSOs with very high mass at low
redshift? A brief discussion of the possible reasons for this is tentatively
pointed out.
