  We use the Karachentseva (1973) ``Catalogue of Very Isolated Galaxies'' to
investigate a candidate list of >100 very isolated early-type galaxies.
Broad-band imaging and low resolution spectroscopy are available for a large
fraction of these candidates and result in a sample of 102 very isolated
early-type galaxies, including 65 ellipticals and 37 S0 galaxies. Many of these
systems are quite luminous and the resulting optical luminosity functions of
the Es and early-types (E+S0s) show no statistical differences when compared to
luminosity functions dominated by group and cluster galaxies. However, whereas
S0s outnumber Es 4:1 in the CfA survey, isolated Es outnumber S0s by nearly
2:1. We conclude that very isolated elliptical galaxies show no evidence for a
different formation and/or evolution process compared to Es formed in groups or
clusters, but that most S0s are formed by a mechanism (e.g., gas stripping)
that occurs only in groups and rich clusters. Our luminosity function results
for ellipticals are consistent with very isolated ellipticals being formed by
merger events, in which no companions remain.
  CHANDRA observations were proposed to test specifically the merger hypothesis
for isolated ellipticals. However, this program has resulted in the observation
of only one isolated early-type galaxy, the S0 KIG 284, which was not detected
at a limit well below that expected for a remnant group of galaxies. Therefore,
the hypothesis remains untested that very isolated elliptical galaxies are the
remains of a compact group of galaxies which completely merged.
