  The aim of the paper is to obtain a description of the selfadjoint subspace
of the one-speed Boltzmann operator. It is proved that this subspace is
nontrivial if the collision integral is polynomial and the multiplication
coefficient has a lattice of gaps. A similar result is shown to hold for the
3-dimensional transport operator.
  Keywords: completely nonselfadjoint, Boltzmann operator, uncertainly
principle.
