  In this note we prove that the maximally defined operator associated with a
class of Dirac-type differential expressions M(Q) is J-self-adjoint with
respect to a proper antilinear conjugation J under the general hypothesis that
the entries of the matrix potential coefficient Q are locally integrable on the
real line.
  The Dirac-type differential expression M(Q) is of significance as it appears
in the Lax formulation of the nonabelian (matrix-valued) focusing nonlinear
Schr\"odinger hierarchy of evolution equations.
