  We discuss a bias present in the calculation of the global luminosity
function
  (LF) which occurs when analysing faint galaxy samples. This effect exists
because of the different spectral energy distributions of galaxies, which are
in turn quantified by the k-corrections. We demonstrate that this bias occurs
because not all galaxy types are visible in the same absolute magnitude range
at a given redshift and it mainly arises at high redshift since it is related
to large k-corrections. We use realistic simulations with observed LFs to
investigate the amplitude of the bias. We also compare our results to the
global LFs derived from Hubble Deep Field-North and -South (HDF) surveys. We
conclude that, as expected, there is no bias in the global LF measured in the
absolute magnitude range where all galaxy types are observable. Beyond this
range the faint-end slope of the global LF can be over/under-estimated
depending on the adopted LF estimator. The effect is larger when the reference
filter in which the global LF is measured, is far from the rest-frame filter in
which galaxies are selected. The fact that LF estimators are differently
affected by this bias implies that the bias is minimal when the different LF
estimators give measurements consistent with one another at the faint-end. For
instance, we show that the estimators are discrepant in the same way both in
the simulated and HDF LFs. This suggests that the HDF LFs are affected by the
presently studied bias. The best solution to avoid this bias is to derive the
global LF in the reference filter closest to the rest-frame selection filter.
