  AIMS: We have compiled one of the largest normal-galaxy samples ever to probe
X-ray luminosity function evolution separately for early and late-type systems.
  METHODS: We selected 207 normal galaxies up to redshift z~1.4, with data from
four major Chandra X-ray surveys, namely the Chandra deep fields (north, south
and extended) and XBootes, and a combination of X-ray and optical criteria. We
used template spectral energy-distribution fitting to obtain separate early-
and late-type sub-samples, made up of 101 and 106 systems, respectively. For
the full sample, as well as the two sub-samples, we obtained luminosity
functions using both a non-parametric and a parametric, maximum-likelihood
method.
  RESULTS: For the full sample, the non-parametric method strongly suggests
luminosity evolution with redshift. The maximum-likelihood estimate shows that
this evolution follows ~(1+z)^k_total, k_total=2.2+-0.3. For the late-type
sub-sample, we obtained k_late=2.4^+1.0_-2.0. We detected no significant
evolution in the early-type sub-sample. The distributions of early and
late-type systems with redshift show that late types dominate at z>~0.5 and
hence drive the observed evolution for the total sample.
  CONCLUSIONS: Our results support previous results in X-ray and other
wavebands, which suggests luminosity evolution with k=2-3.
