  We present an analysis of the XMM-Newton and Chandra ACIS-S observations of
the LINER nucleus of the Sombrero galaxy and we discuss possible explanations
for its very sub-Eddington luminosity by complementing the X-ray results with
high angular resolution observations in other bands. The X-ray investigation
shows a hard (Gamma=1.89) and moderately absorbed (N_H=1.8 10^21 cm^-2) nuclear
source of 1.5 10^40 erg s^-1 in the 2-10 keV band, surrounded by hot gas at a
temperature of \sim 0.6 keV. The bolometric nuclear luminosity is at least \sim
200 times lower than expected if mass accreted on the supermassive black hole,
that HST shows to reside at the center of this galaxy, at the rate predicted by
the spherical and adiabatic Bondi accretion theory and with the high radiative
efficiency of a standard accretion disc. The low luminosity, coupled to the
observed absence of Fe-K emission in the nuclear spectrum, indicates that such
a disc is not present. This nucleus differs from bright unobscured AGNs also
for the lack of high flux variability and of prominent broad Halpha emission.
However, it is also too faint for the predictions of simple radiatively
inefficient accretion taking place at the Bondi rate; it could be too radio
bright, instead, for radiatively inefficient accretion that includes strong
mass outflows or convection. This discrepancy could be solved by the possible
presence of nuclear radio jets. An alternative explanation of the low
luminosity, in place of radiative inefficiency, could be unsteady accretion.
