  Assuming 3 neutrino mixing and massive Majorana neutrinos, we analyze the
implications of the results of the solar neutrino experiments, including the
latest SNO data, which favor the LMA MSW solution of the solar neutrino problem
with \tan^2 \theta_sol < 1, for the predictions of the effective Majorana mass
|<m>| in neutrinoless double beta decay. For \cos (2 \theta_sol) \geq 0.26,
which follows from the analysis of the new solar neutrino data, we find
significant lower limits on |<m>| in the cases of quasi-degenerate and inverted
hierarchy neutrino mass spectrum, |<m>| \geq 0.035 eV and |<m>| \geq 8.5 10^-3
eV, respectively. If the spectrum is hierarchical the upper limit holds |<m>|
\leq 8.2 10^-3 eV. Correspondingly, not only a measured value of |<m>| \neq 0,
but even an experimental upper limit on |<m>| of the order of few 10^-2 eV can
provide information on the type of the neutrino mass spectrum; it can provide
also a significant upper limit on the mass of the lightest neutrino m1. A
measured value of |<m>| \geq 0.2 eV, combined with data on neutrino masses from
the tritium beta-decay experiment KATRIN might allow to establish whether the
CP-symmetry is violated in the lepton sector.
