  The epsilon-enlargement of a maximal monotone operator is a construct similar
to the Br{\o}ndsted and Rocakfellar epsilon-subdifferential enlargement of the
subdifferential. Like the epsilon-subdifferential, the epsilon-enlargement of a
maximal monotone operator has practical and theoretical applications.
  In a recent paper in Journal of Convex Analysis Burachik and Iusem studied
conditions under which a maximal monotone operator is non-enlargeable, that is,
its epsilon-enlargement coincides with the operator. Burachik and Iusem studied
these non-enlargeable operators in reflexive Banach spaces, assuming the
interior of the domain of the operator to be nonempty. In the present work, we
remove the assumption on the domain of non-enlargeable operators and also
present partial results for the non-reflexive case.
