  Using the Dirac-Brueckner-Hartree-Fock (DBHF) approach including the hyperon
degrees of freedom, we investigate the properties of neutron-star matter. To
handle the hyperons in matter, we first examine the importance of the space
part of baryon self-energies at high densities, and secondly study the effect
of negative-energy states of baryons, which can provide an unambiguous
relationship between the in-medium reaction matrices for baryon-baryon
scattering and the baryon self-energies. We solve the coupled, Bethe-Salpeter
equations in the nuclear-matter rest frame by using the Bonn potentials. We
assume that eight kinds of nonstrange and strange mesons
($\sigma,\,\delta,\,\omega,\,\rho,\,\eta,\,\pi,\,K,\,K^{\ast}$) take part in
the interactions between two baryons. Then, we calculate the baryon
self-energies, the energy density and pressure of matter. The present
calculation provides a hard equation of state in neutron-star matter at high
densities, which is generated by the effect of Pauli exclusion, the short-range
correlations between two baryons, etc. We finally predict the maximum
neutron-star mass of $2.02\,M_{\odot}$, which is consistent with both the
recently observed masses, $1.97\pm0.04M_{\odot}$ (J1614-2230) and
$2.01\pm0.04M_{\odot}$ (J0348+0432).
